Hard disks: A Window into the World of Stat Physics

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==References== ==References==
-References are accessible via our github server, but here they are again, for easy reference.+References are accessible via our github server.
- +
-# article section:+
- +
-@article{Alder1957,+
- author = {{Alder}, B.~J. and {Wainwright}, T.~E.},+
- title = "{Phase Transition for a Hard Sphere System}",+
- journal = {\jcp},+
- year = 1957,+
- month = nov,+
- volume = 27,+
- pages = {1208-1209},+
- doi = {10.1063/1.1743957},+
- adsurl = {http://adsabs.harvard.edu/abs/1957JChPh..27.1208A},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{Alder1962,+
- author = {{Alder}, B.~J. and {Wainwright}, T.~E.},+
- title = "{Phase Transition in Elastic Disks}",+
- journal = {Physical Review},+
- year = 1962,+
- month = jul,+
- volume = 127,+
- pages = {359-361},+
- doi = {10.1103/PhysRev.127.359},+
- adsurl = {http://adsabs.harvard.edu/abs/1962PhRv..127..359A},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{AlderWainwright1959,+
- author = {{Alder}, B.~J. and {Wainwright}, T.~E.},+
- title = "{Studies in Molecular Dynamics. I. General Method}",+
- journal = {\jcp},+
- year = 1959,+
- month = aug,+
- volume = 31,+
- pages = {459-466},+
- doi = {10.1063/1.1730376},+
- adsurl = {http://adsabs.harvard.edu/abs/1959JChPh..31..459A},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{AlderWainwrightAutocorrelation1970,+
- title = {Decay of the Velocity Autocorrelation Function},+
- author = {Alder, B. J. and Wainwright, T. E.},+
- journal = {Phys. Rev. A},+
- volume = {1},+
- issue = {1},+
- pages = {18--21},+
- numpages = {0},+
- year = {1970},+
- month = {Jan},+
- publisher = {American Physical Society},+
- doi = {10.1103/PhysRevA.1.18},+
- url = {http://link.aps.org/doi/10.1103/PhysRevA.1.18}+
-}+
- +
-@article{Asakura1954,+
- author = {{Asakura}, S. and {Oosawa}, F.},+
- title = "{On Interaction between Two Bodies Immersed in a Solution of Macromolecules}",+
- journal = {\jcp},+
- year = 1954,+
- month = jul,+
- volume = 22,+
- pages = {1255-1256},+
- doi = {10.1063/1.1740347},+
- adsurl = {http://adsabs.harvard.edu/abs/1954JChPh..22.1255A},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{BannermanLue2010,+
- author = {{Bannerman}, M.~N. and {Lue}, L.},+
- title = "{Exact on-event expressions for discrete potential systems}",+
- journal = {\jcp},+
- year = 2010,+
- month = sep,+
- volume = 133,+
- number = 12,+
- pages = {124506-124506},+
- doi = {10.1063/1.3486567},+
- adsurl = {http://adsabs.harvard.edu/abs/2010JChPh.133l4506B},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{Bernard2009,+
- title = {Event-chain Monte Carlo algorithms for hard-sphere systems},+
- author = {Bernard, E. P. and Krauth, W. and Wilson, D. B.},+
- journal = {Phys. Rev. E},+
- volume = {80},+
- issue = {5},+
- pages = {056704},+
- numpages = {5},+
- year = {2009},+
- month = {Nov},+
- publisher = {American Physical Society},+
- doi = {10.1103/PhysRevE.80.056704},+
- url = {http://link.aps.org/doi/10.1103/PhysRevE.80.056704}+
-}+
- +
-@article{Bernard2011,+
- title = {Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition},+
- author = {Bernard, E. P. and Krauth, W.},+
- journal = {Phys. Rev. Lett.},+
- volume = {107},+
- issue = {15},+
- pages = {155704},+
- numpages = {4},+
- year = {2011},+
- month = {Oct},+
- publisher = {American Physical Society},+
- doi = {10.1103/PhysRevLett.107.155704},+
- url = {http://link.aps.org/doi/10.1103/PhysRevLett.107.155704}+
-}+
- +
-@article{BernardChanalKrauth2010,+
- author = {{Bernard}, E.~P. and {Chanal}, C. and {Krauth}, W.},+
- title = "{Damage spreading and coupling in Markov chains}",+
- journal = {EPL (Europhysics Letters)},+
-archivePrefix = "arXiv",+
- eprint = {1010.1195},+
- primaryClass = "cond-mat.stat-mech",+
- year = 2010,+
- month = dec,+
- volume = 92,+
- pages = {60004},+
- doi = {10.1209/0295-5075/92/60004},+
- adsurl = {http://adsabs.harvard.edu/abs/2010EL.....9260004B},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{BernardKrauth2011,+
- title = {Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition},+
- author = {Bernard, Etienne P. and Krauth, Werner},+
- journal = PRL,+
- volume = {107},+
- issue = {15},+
- pages = {155704},+
- numpages = {4},+
- year = {2011},+
- month = {Oct},+
- publisher = {American Physical Society},+
- doi = {10.1103/PhysRevLett.107.155704},+
- url = {http://link.aps.org/doi/10.1103/PhysRevLett.107.155704}+
-}+
- +
-@article{Bianchi2012JCP,+
- author = {Bianchi, E. and Doppelbauer, G. and Filion, L. and Dijkstra, M. and Kahl, G.},+
- title = {Predicting patchy particle crystals: Variable box shape simulations and evolutionary algorithms},+
- journal = {J. Chem. Phys.},+
- year = {2012},+
- volume = {136},+
- number = {21}, +
- pages = {214102},+
- url = {http://scitation.aip.org/content/aip/journal/jcp/136/21/10.1063/1.4722477},+
- doi = {10.1063/1.4722477} +
-}+
- +
-@article{ChanalKrauth2010,+
- author = {{Chanal}, C. and {Krauth}, W.},+
- title = "{Convergence and coupling for spin glasses and hard spheres}",+
- journal = {\pre},+
-archivePrefix = "arXiv",+
- eprint = {0910.1530},+
- primaryClass = "cond-mat.stat-mech",+
- keywords = {Computational techniques, simulations, Boson systems},+
- year = 2010,+
- month = jan,+
- volume = 81,+
- number = 1,+
- eid = {016705},+
- pages = {016705},+
- doi = {10.1103/PhysRevE.81.016705},+
- adsurl = {http://adsabs.harvard.edu/abs/2010PhRvE..81a6705C},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{Chen1999,+
- author = {Fang Chen and László Lovász and Igor Pak},+
- title = {Lifting Markov Chains to Speed up Mixing},+
- journal = {Proceedings of the 17th Annual ACM Symposium on Theory of Computing},+
- pages = {275},+
- year = {1999},+
-}+
- +
-@article{DeGraag2012JCP,+
- author = "de Graaf, J. and Filion, L. and Marechal, M. and van Roij, R. and Dijkstra, M.",+
- title = "Crystal-structure prediction via the Floppy-Box Monte Carlo algorithm: Method and application to hard (non)convex particles",+
- journal = "J. Chem. Phys.",+
- year = "2012",+
- volume = "137",+
- number = "21", +
- pages = "214101",+
- doi = "10.1063/1.4767529",+
- url = "http://scitation.aip.org/content/aip/journal/jcp/137/21/10.1063/1.4767529",+
-}+
- +
-@article{Diaconis2000,+
- author ={Diaconis, P. and Holmes, S. and Neal, R.\ M.},+
- journal = {Annals of Applied Probability},+
- volume = {10},+
- pages = {726},+
- year = {2000}+
-}+
- +
-@article{Engel2013,+
- title = {Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods},+
- author = {Engel, M. and Anderson, J. A. and Glotzer, S. C. and Isobe, M. and Bernard, E. P. and Krauth, W.},+
- journal = {Phys. Rev. E},+
- volume = {87},+
- issue = {4},+
- pages = {042134},+
- numpages = {8},+
- year = {2013},+
- month = {Apr},+
- publisher = {American Physical Society},+
- doi = {10.1103/PhysRevE.87.042134},+
- url = {http://link.aps.org/doi/10.1103/PhysRevE.87.042134}+
-}+
- +
-@article{FeanyBender2000,+
- author = {{Feany}, M.~B. and {Bender}, W. W.},+
- title = "{A Drosophila model of Parkinson's disease}",+
- journal = {Nature},+
- year = 2000,+
- volume = 404,+
- pages = {394-398}+
-}+
- +
-@article{Gibson2015,+
- title = "Behavioral Responses to a Repetitive Visual Threat Stimulus Express a Persistent State of Defensive Arousal in Drosophila ",+
- journal = "Current Biology ",+
- volume = "25",+
- number = "11",+
- pages = "1401 - 1415",+
- year = "2015",+
- note = "",+
- issn = "0960-9822",+
- doi = "http://dx.doi.org/10.1016/j.cub.2015.03.058",+
- url = "//www.sciencedirect.com/science/article/pii/S096098221500411X",+
- author = "William T. Gibson and Carlos R. Gonzalez and Conchi Fernandez and Lakshminarayanan Ramasamy and Tanya Tabachnik and Rebecca R. Du and Panna D. Felsen and Michael R. Maire and Pietro Perona and David J. Anderson"+
-}+
- +
-@article{HagenPagonabarrangaLoweFrenkel1997,+
- title = {Algebraic Decay of Velocity Fluctuations in a Confined Fluid},+
- author = {Hagen, M. H. J. and Pagonabarraga, I. and Lowe, C. P. and Frenkel, D.},+
- journal = {Phys. Rev. Lett.},+
- volume = {78},+
- issue = {19},+
- pages = {3785-3788},+
- numpages = {0},+
- year = {1997},+
- month = {May},+
- publisher = {American Physical Society},+
- doi = {10.1103/PhysRevLett.78.3785},+
- url = {http://link.aps.org/doi/10.1103/PhysRevLett.78.3785}+
-}+
- +
-@article{Ising1925,+
- author={Ising, Ernst},+
- title={Beitrag zur Theorie des Ferromagnetismus},+
- journal={Zeitschrift f\"ur Physik},+
- year={1925},+
- volume={31},+
- number={1},+
- pages={253-258},+
- issn={0044-3328},+
- doi={10.1007/BF02980577},+
- url={http://dx.doi.org/10.1007/BF02980577}+
-}+
- +
-@article{Isobe1999,+
- author = {{Isobe}, M.},+
- title = "{Simple and Efficient Algorithm for Large Scale Molecular Dynamics Simulation in Hard Disk System}",+
- journal = {International Journal of Modern Physics C},+
- eprint = {physics/9907025},+
- keywords = {Event-driven molecular dynamics, Hard disk system, Algorithm},+
- year = 1999,+
- volume = 10,+
- pages = {1281-1293},+
- doi = {10.1142/S0129183199001042},+
- adsurl = {http://adsabs.harvard.edu/abs/1999IJMPC..10.1281I},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{Kapfer2015PRL,+
- title = {Two-Dimensional Melting: From Liquid-Hexatic Coexistence to Continuous Transitions},+
- author = {Kapfer, S. C. and Krauth, W.},+
- journal = {Phys. Rev. Lett.},+
- volume = {114},+
- issue = {3},+
- pages = {035702},+
- numpages = {5},+
- year = {2015},+
- month = {Jan},+
- publisher = {American Physical Society},+
- doi = {10.1103/PhysRevLett.114.035702},+
- url = {http://link.aps.org/doi/10.1103/PhysRevLett.114.035702}+
-}+
- +
-@article{Kirkpatrick1983,+
- url = {http://www.jstor.org/stable/1690046},+
- author = {S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi},+
- journal = {Science},+
- number = {4598},+
- pages = {671-680},+
- publisher = {American Association for the Advancement of Science},+
- title = {Optimization by Simulated Annealing},+
- volume = {220},+
- year = {1983}+
-}+
- +
-@article{KirkwoodMonroe1941,+
- author = {{Kirkwood}, J.~G. and {Monroe}, E.},+
- title = "{Statistical Mechanics of Fusion}",+
- journal = {\jcp},+
- year = 1941,+
- month = jul,+
- volume = 9,+
- pages = {514-526},+
- doi = {10.1063/1.1750949},+
- adsurl = {http://adsabs.harvard.edu/abs/1941JChPh...9..514K},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{KosterlitzThouless1973,+
- author = {{Kosterlitz}, J.~M. and {Thouless}, D.~J.},+
- title = "{Ordering, metastability and phase transitions in two-dimensional systems}",+
- journal = {Journal of Physics C Solid State Physics},+
- year = 1973,+
- month = apr,+
- volume = 6,+
- pages = {1181-1203},+
- doi = {10.1088/0022-3719/6/7/010},+
- adsurl = {http://adsabs.harvard.edu/abs/1973JPhC....6.1181K},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{Kramers1941,+
- author = {{Kramers}, H.~A. and {Wannier}, G.~H.},+
- title = "{Statistics of the Two-Dimensional Ferromagnet. Part I}",+
- journal = {Physical Review},+
- year = 1941,+
- month = aug,+
- volume = 60,+
- pages = {252-262},+
- doi = {10.1103/PhysRev.60.252},+
- adsurl = {http://adsabs.harvard.edu/abs/1941PhRv...60..252K},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{KramersWannier1941,+
- title = {Statistics of the Two-Dimensional Ferromagnet. Part I},+
- author = {Kramers, H. A. and Wannier, G. H.},+
- journal = {Phys. Rev.},+
- volume = {60},+
- issue = {3},+
- pages = {252--262},+
- numpages = {0},+
- year = {1941},+
- month = {Aug},+
- publisher = {American Physical Society},+
- doi = {10.1103/PhysRev.60.252},+
- url = {http://link.aps.org/doi/10.1103/PhysRev.60.252}+
-}+
- +
-@article{LebowitzPenrose1964,+
- author = {{Lebowitz}, J.~L. and {Penrose}, O.},+
- title = "{Convergence of Virial Expansions}",+
- journal = {Journal of Mathematical Physics},+
- year = 1964,+
- month = jul,+
- volume = 5,+
- pages = {841-847},+
- doi = {10.1063/1.1704186},+
- adsurl = {http://adsabs.harvard.edu/abs/1964JMP.....5..841L},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{Lenz1920,+
- author="Lenz, Wilhelm",+
- title="XXXX",+
- journal="Physikalische Zeitschrift",+
- year="1920",+
- volume="21",+
- pages="613",+
-}+
- +
-@article{Levy1940,+
- Author = {P. {L\'evy}},+
- Title = {Sur certains processus stochastiques homog\`enes.},+
- Journal = {{Compos. Math.}},+
- ISSN = {0010-437X; 1570-5846/e},+
- Volume = {7},+
- Pages = {283--339},+
- Year = {1939},+
- Publisher = {Cambridge University Press, Cambridge; London Mathematical Society, London},+
- MSC2010 = {60Gxx},+
- Zbl = {0022.05903}+
-}+
- +
-@article{Mermin1966,+
- author = {{Mermin}, N.~D. and {Wagner}, H.},+
- title = "{Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models}",+
- journal = {Physical Review Letters},+
- year = 1966,+
- month = nov,+
- volume = 17,+
- pages = {1133-1136},+
- doi = {10.1103/PhysRevLett.17.1133},+
- adsurl = {http://adsabs.harvard.edu/abs/1966PhRvL..17.1133M},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{Metropolis1953,+
- author = {{Metropolis}, N. and {Rosenbluth}, A.~W. and {Rosenbluth}, M.~N. and {Teller}, A.~H. and {Teller}, E.},+
- title = "{Equation of State Calculations by Fast Computing Machines}",+
- journal = {\jcp},+
- year = 1953,+
- month = jun,+
- volume = 21,+
- pages = {1087-1092},+
- doi = {10.1063/1.1699114},+
- adsurl = {http://adsabs.harvard.edu/abs/1953JChPh..21.1087M},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{Metropolis1953JCP,+
- author = "Metropolis, N. and Rosenbluth, A. W. and Rosenbluth, M. N. and Teller, A. H. and Teller, E.",+
- title = "Equation of State Calculations by Fast Computing Machines",+
- journal = "J. Chem. Phys.",+
- year = "1953",+
- volume = "21",+
- number = "6", +
- pages = "1087-1092",+
- url = "http://scitation.aip.org/content/aip/journal/jcp/21/6/10.1063/1.1699114",+
- doi = "10.1063/1.1699114" +
-}+
- +
-@article{Mickel2013,+
- author = "Mickel, W. and Kapfer, S. C. and Schr{\"o}der-Turk, G. E. and Mecke, K.",+
- title = "Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter",+
- journal = "J. Chem. Phys.",+
- year = "2013",+
- volume = "138",+
- number = "4", +
- pages = 044501,+
- url = "http://scitation.aip.org/content/aip/journal/jcp/138/4/10.1063/1.4774084",+
- doi = "10.1063/1.4774084" +
-}+
- +
-@article{Mladek2006PRL,+
- title = {Formation of Polymorphic Cluster Phases for a Class of Models of Purely Repulsive Soft Spheres},+
- author = {Mladek, B. M. and Gottwald, D. and Kahl, G. and Neumann, M. and Likos, C. N.},+
- journal = {Phys. Rev. Lett.},+
- volume = {96},+
- issue = {4},+
- pages = {045701},+
- numpages = {4},+
- year = {2006},+
- month = {Jan},+
- publisher = {American Physical Society},+
- doi = {10.1103/PhysRevLett.96.045701},+
- url = {http://link.aps.org/doi/10.1103/PhysRevLett.96.045701}+
-}+
- +
-@article{Mladek2006PRLerratum,+
- title = {Erratum: Formation of Polymorphic Cluster Phases for a Class of Models of Purely Repulsive Soft Spheres [Phys. Rev. Lett. \textbf{96} , 045701 (2006)]},+
- author = {Mladek, B. M. and Gottwald, D. and Kahl, G. and Neumann, M. and Likos, C. N.},+
- journal = {Phys. Rev. Lett.},+
- volume = {97},+
- issue = {1},+
- pages = {019901},+
- numpages = {1},+
- year = {2006},+
- month = {Jul},+
- publisher = {American Physical Society},+
- doi = {10.1103/PhysRevLett.97.019901},+
- url = {http://link.aps.org/doi/10.1103/PhysRevLett.97.019901}+
-}+
- +
-@article{Onsager1944,+
- author = {{Onsager}, L.},+
- title = "{Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition}",+
- journal = {Physical Review},+
- year = 1944,+
- month = feb,+
- volume = 65,+
- pages = {117-149},+
- doi = {10.1103/PhysRev.65.117},+
- adsurl = {http://adsabs.harvard.edu/abs/1944PhRv...65..117O},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{Peierls1936,+
- author = {Peierls, R.},+
- title = {On {Ising's} model of ferromagnetism},+
- journal = {Mathematical Proceedings of the Cambridge Philosophical Society},+
- volume = {32},+
- issue = {03},+
- month = {10},+
- year = {1936},+
- issn = {1469-8064},+
- pages = {477--481},+
- numpages = {5},+
- doi = {10.1017/S0305004100019174},+
- URL = {http://journals.cambridge.org/article_S0305004100019174},+
-}+
- +
-@article{PomeauResibois1975,+
- title = {Time dependent correlation functions and mode-mode coupling theories},+
- journal = {Physics Reports},+
- volume = {19},+
- number = {2},+
- pages = {63 - 139},+
- year = {1975},+
- issn = {0370-1573},+
- doi = "http://dx.doi.org/10.1016/0370-1573(75)90019-8",+
- url = "http://www.sciencedirect.com/science/article/pii/0370157375900198",+
- author = {Pomeau, Y. and Résibois, P.},+
-}+
- +
-@article{Rapaport1980,+
- author = {{Rapaport}, D.~C.},+
- title = "{The Event Scheduling Problem in Molecular Dynamic Simulation}",+
- journal = {Journal of Computational Physics},+
- year = 1980,+
- month = feb,+
- volume = 34,+
- pages = {184-201},+
- doi = {10.1016/0021-9991(80)90104-7},+
- adsurl = {http://adsabs.harvard.edu/abs/1980JCoPh..34..184R},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{RevModPhys.47.773,+
- title = {The renormalization group: Critical phenomena and the Kondo problem},+
- author = {Wilson, Kenneth G.},+
- journal = {Rev. Mod. Phys.},+
- volume = {47},+
- issue = {4},+
- pages = {773--840},+
- numpages = {0},+
- year = {1975},+
- month = {Oct},+
- publisher = {American Physical Society},+
- doi = {10.1103/RevModPhys.47.773},+
- url = {http://link.aps.org/doi/10.1103/RevModPhys.47.773}+
-}+
- +
-@article{Simanyi2003,+
- author = {{Sim{\'a}nyi}, N.},+
- title = "{Proof of the Boltzmann-Sinai ergodic hypothesis for typical hard disk systems}",+
- journal = {Inventiones Mathematicae},+
- eprint = {math/0210280},+
- year = 2003,+
- month = oct,+
- volume = 154,+
- pages = {123-178},+
- doi = {10.1007/s00222-003-0304-9},+
- adsurl = {http://adsabs.harvard.edu/abs/2003InMat.154..123S},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{Sinai1963,+
- author = {{Sinai}, Y.~G.},+
- title = "{Some Remarks on the Spectral Properties of Ergodic Dynamical Systems}",+
- journal = {Russian Mathematical Surveys},+
- year = 1963,+
- month = oct,+
- volume = 18,+
- pages = {37-50},+
- doi = {10.1070/RM1963v018n05ABEH004131},+
- adsurl = {http://adsabs.harvard.edu/abs/1963RuMaS..18...37S},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{Sinai1970,+
- author = {{Sinai}, Y.~G.},+
- title = "{Dynamical systems with elastic reflections}",+
- journal = {Russian Mathematical Surveys},+
- year = 1970,+
- month = apr,+
- volume = 25,+
- pages = {137-189},+
- doi = {10.1070/RM1970v025n02ABEH003794},+
- adsurl = {http://adsabs.harvard.edu/abs/1970RuMaS..25..137S},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-@article{Steinhardt1983PRB,+
- title = {Bond-orientational order in liquids and glasses},+
- author = {Steinhardt, P. J. and Nelson, D. R. and Ronchetti, M.},+
- journal = {Phys. Rev. B},+
- volume = {28},+
- issue = {2},+
- pages = {784--805},+
- numpages = {0},+
- year = {1983},+
- month = {Jul},+
- publisher = {American Physical Society},+
- doi = {10.1103/PhysRevB.28.784},+
- url = {http://link.aps.org/doi/10.1103/PhysRevB.28.784}+
-}+
- +
-@article{Swope1992PRA,+
- title = {Thermodynamics, statistical thermodynamics, and computer simulation of crystals with vacancies and interstitials},+
- author = {Swope, W. C. and Andersen, H. C.},+
- journal = {Phys. Rev. A},+
- volume = {46},+
- issue = {8},+
- pages = {4539--4548},+
- numpages = {0},+
- year = {1992},+
- month = {Oct},+
- publisher = {American Physical Society},+
- doi = {10.1103/PhysRevA.46.4539},+
- url = {http://link.aps.org/doi/10.1103/PhysRevA.46.4539}+
-}+
- +
-@article{WilliamsBryantSnookvanMegen2006,+
- title = {Velocity Autocorrelation Functions of Hard-Sphere Fluids: Long-Time Tails upon Undercooling},+
- author = {Williams, Stephen R. and Bryant, G. and Snook, I. K. and van Megen, W.},+
- journal = {Phys. Rev. Lett.},+
- volume = {96},+
- issue = {8},+
- pages = {087801},+
- numpages = {4},+
- year = {2006},+
- month = {Feb},+
- publisher = {American Physical Society},+
- doi = {10.1103/PhysRevLett.96.087801},+
- url = {http://link.aps.org/doi/10.1103/PhysRevLett.96.087801}+
-}+
- +
-@article{Wilson2000,+
- author = {Wilson, David Bruce},+
- title = {How to couple from the past using a read-once source of randomness},+
- journal = {Random Structures \& Algorithms},+
- volume = {16},+
- number = {1},+
- publisher = {John Wiley \& Sons, Inc.},+
- issn = {1098-2418},+
- url = {http://dx.doi.org/10.1002/(SICI)1098-2418(200001)16:1<85::AID-RSA6>3.0.CO;2-H},+
- doi = {10.1002/(SICI)1098-2418(200001)16:1<85::AID-RSA6>3.0.CO;2-H},+
- pages = {85--113},+
- year = {2000}+
-}+
- +
-@article{WittmerPolinska2011,+
- author = {{Wittmer}, J.~P. and {Poli{\'n}ska}, P. and {Meyer}, H. and {Farago}, J. and {Johner}, A. and {Baschnagel}, J. and {Cavallo}, A. },+
- title = "{Scale-free center-of-mass displacement correlations in polymer melts without topological constraints and momentum conservation: A bond-fluctuation model study}",+
- journal = {\jcp},+
-archivePrefix = "arXiv",+
- eprint = {1102.4962},+
- primaryClass = "cond-mat.soft",+
- keywords = {momentum, Monte Carlo methods, polymer melts, Polymer melts and blends, Computer simulation of liquid structure, Time-dependent properties, relaxation, Monte Carlo methods},+
- year = 2011,+
- month = jun,+
- volume = 134,+
- number = 23,+
- pages = {234901-234901},+
- doi = {10.1063/1.3601918},+
- adsurl = {http://adsabs.harvard.edu/abs/2011JChPh.134w4901W},+
- adsnote = {Provided by the SAO/NASA Astrophysics Data System}+
-}+
- +
-################################################################################+
-# book section:+
- +
-@book{Bernoulli1738,+
- title="Hydrodynamica",+
- author="Bernoulli, Daniel", +
- year={1738},+
- url="http://dx.doi.org/10.3931/e-rara-3911"+
-}+
- +
-@book{Conway1999,+
- author={J. H. Conway \and N. J. A. Sloane},+
- title={Sphere Packings, Lattices and Groups},+
- publisher={Springer-Verlag},+
- address={New York},+
- year={1999},+
-}+
- +
-@book{Feynman1972,+
- title={Statistical mechanics: a set of lectures},+
- author={Feynman, R. P.},+
- series={Frontiers in physics},+
- year={1972},+
- publisher={W. A. Benjamin, Reading, Massachusetts.}+
-}+
- +
-@book{Pathria2011,+
- title={Statistical Mechanics},+
- author={Pathria, R.K. and Beale, P.D.},+
- isbn={9780123821898},+
- year={2011},+
- publisher={Elsevier Science}+
-}+
- +
-@book{SMAC,+
- title={Statistical Mechanics: Algorithms and Computations},+
- publisher={Oxford University Press, {USA}},+
- author={Krauth, W.},+
- month={nov},+
- year={2006},+
- url = "www.smac.lps.ens.fr"+
-}+
- +
-@book{Sethna2006,+
- title={Statistical mechanics: entropy, order parameters, and complexity},+
- author={Sethna, J.},+
- volume={14},+
- year={2006},+
- publisher={Oxford University Press}+
-}+
- +
-@book{Szasz2000,+
- editor={D. Sz\'{a}sz},+
- title={Hard Ball Systems and the Lorentz Gas},+
- publisher={Springer-Verlag},+
- address={Berlin Heidelberg},+
- year={2000},+
-}+
- +
-@book{Weaire2000,+
- author={T. Aste and D. Weaire},+
- title={The pursuit of perfect packing},+
- publisher={Institute of Physics Publishing},+
- address={Bristol},+
- year={2000},+
-}+
- +
-################################################################################+
-# incollection section:+
- +
-@incollection{Barber1983,+
- author = "Barber, M. N.",+
- title = "Finite-size scaling",+
- booktitle = "Phase transitions and Critical Phenomena",+
- editor = "Comb, C. and Lebowitz, J. L.",+
- publisher = "Academic, New York",+
- year = 1983,+
-}+
- +
-@incollection{FriggHartmann2016,+
- author = {Frigg, Roman and Hartmann, Stephan},+
- title = {Models in Science},+
- booktitle = {The Stanford Encyclopedia of Philosophy},+
- editor = {Edward N. Zalta},+
- howpublished = {\url{https://plato.stanford.edu/archives/win2016/entries/models-science/}},+
- year = {2016},+
- edition = {Winter 2016},+
- publisher = {Metaphysics Research Lab, Stanford University}+
-}+
- +
-@incollection{vonNeumann1951,+
- author = "{von} Neumann, J.",+
- title = "Various techniques used in connection with random digits",+
- booktitle = "The Monte Carlo Method",+
- year = "1951",+
- publisher = "United States Government Printing Office",+
- address = "Washington, DC",+
- series = "National Bureau of Standards Applied Mathematics Series",+
- number = "12",+
- pages = "36-38"+
-}+
- +
-################################################################################+
-# phdthesis section:+
- +
-@phdthesis{Piatecki2014PHD,+
- author={S. Piatecki},+
- year={2014},+
- title={The Bose gas at large scattering lengths},+
- school={\'Ecole Normale Sup\'erieure, Paris},+
- url={https://tel.archives-ouvertes.fr/tel-01158248}+
-}+
- +
-################################################################################+
-# unpublished section:+
- +
-@unpublished{Comparin2016b,+
- author = {Comparin, T. and Krauth, W.},+
- title = {},+
- note = {in preparation}+
-}+

Current revision

This is the homepage for the Lecture series on Hard disks: A Window into the World of Statistical Physics given in January and February 2017 at the University of Tokyo as an intensive graduate lecture course in the School of Sciences.

Look here for practical information


Contents

[edit]

Course Title

Hard Disks: A Window into the World of Statistical Physics

[edit]

Course Objectives/Overview

The hard-disk model has exerted outstanding influence on statistical physics, starting with the first ever N-body calculation in science, by D. Bernoulli (1738), and leading up to its role in the very definition of statistical mechanics, by Maxwell and Boltzmann, and to the formal proof of the validity of statistical mechanics, by Sinai (1970). Decades ago, hard disks were the first system to be studied by Markov-chain Monte Carlo methods (Metropolis et al, 1953) and by molecular dynamics (Alder and Wainwright, 1957). Up to the present day, the model has continued to drive the development of algorithms (Bernard et al, 2009), including the "Beyond-Metropolis" approach (Michel et al, 2014). It was in hard disks, through numerical simulations, that a two-dimensional melting transition was first seen to occur (Alder and Wainwright, 1962) even though such systems cannot develop long-range crystalline order (Mermin and Wagner, 1966). This provided the starting point for the Kosterlitz-Thouless theory (1973), although the hard-disk phase diagram was established only recently (Bernard and Krauth, 2011), thus providing a clear view on the physics of phase transitions in two dimensions.

The objective of this course will thus be to discuss the aforementioned central topics of statistical physics from the unique vantage point of the hard-disk model, and in a self-contained way that will be accessible to a wide audience. Overall, the course will introduce to a variety of approaches, from rigorous mathematics to statistics, and from algorithm design and numerical simulations to the theory of phase transitions and to Kosterlitz-Thouless physics and to the interpretation of experiment. It is intended to show how the hard-disk model has continued to shape our view of the physical world, to teach us key aspects, and to prepare for general progress in science.

[edit]

Day 1: Hard disks in classical and statistical mechanics (January 24, 2017. First part: Lectures 1-3)

  • Introduction
    1. Overview of this course
    2. Practical matters
    3. Models and Theories: A clarification
      1. Fruit fly "drosophila melanogaster"
      2. Two-dimensional Ising model
      3. Hard-disk model
  1. Molecular dynamics - Newtonian mechanics
    1. Event-driven Molecular dynamics
    2. Long-time tails in molecular dynamics
    3. Algorithms and data structures
  2. Monte Carlo sampling - Boltzmann mechanics
    1. Direct sampling
    2. Markov-chain sampling
      1. Long-time tails in Monte Carlo dynamics
    3. Perfect sampling: Coupling from the past, Wilson's algorithm for hard disks
  3. Statistics of deterministic dynamics
  4. Determinism and unpredictability
[edit]

Day 2: Hard disks and thermodynamical phases (January 26, 2017. First part: Lectures 4-7)

[edit]

Day 3: Hard disks and Markov chains (January 31, 2017. Second part: Lectures 1-3)

[edit]

Day 4: Hard disks and two-dimensional melting (February 2, 2017. Second part: Lectures 4-7)

[edit]

Keywords of the Course

Statistical mechanics, computational physics, phase transitions, colloids, melting transition, Monte Carlo algorithms, Molecular dynamics, Kosterlitz-Thouless transition.

[edit]

References

References are accessible via our github server.

Retrieved from "http://www.lps.ens.fr/~krauth/index.php/Hard_disks:_A_Window_into_the_World_of_Stat_Physics"
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