laboratoire de physique statistique
 
 
laboratoire de physique statistique

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2016
Cell-veto Monte Carlo algorithm for long-range systems - Kapfer, Sebastian C. and Krauth, Werner
PHYSICAL REVIEW E 94 (2016) 
LPS


Abstract : We present a rigorous efficient event-chain Monte Carlo algorithm for long-range interacting particle systems. Using a cell-veto scheme within the factorized Metropolis algorithm, we compute each single-particle move with a fixed number of operations. For slowly decaying potentials such as Coulomb interactions, screening line charges allow us to take into account periodic boundary conditions. We discuss the performance of the cell-veto Monte Carlo algorithm for general inverse-power-law potentials, and illustrate how it provides a new outlook on one of the prominent bottlenecks in large-scale atomistic Monte Carlo simulations.
Momentum Distribution in the Unitary Bose Gas from First Principles - Comparin, Tommaso and Krauth, Werner
PHYSICAL REVIEW LETTERS 117 (2016) 
LPS


Abstract : We consider a realistic bosonic N-particle model with unitary interactions relevant for Efimov physics. Using quantum Monte Carlo methods, we find that the critical temperature for Bose-Einstein condensation is decreased with respect to the ideal Bose gas. We also determine the full momentum distribution of the gas, including its universal asymptotic behavior, and compare this crucial observable to recent experimental data. Similar to the experiments with different atomic species, differentiated solely by a three-body length scale, our model only depends on a single parameter. We establish a weak influence of this parameter on physical observables. In current experiments, the thermodynamic instability of our model from the atomic gas towards an Efimov liquid could be masked by the dynamical instability due to three-body losses.
 
2015
Liquid-solid transitions in the three-body hard-core model - Comparin, Tommaso and Kapfer, Sebastian C. and Krauth, Werner
EPL 109 (2015) 
LPS


Abstract : We determine the phase diagram for a generalisation of two- and three-dimensional hard spheres: a classical system with three-body interactions realised as a hard cut-off on the mean-square distance for each triplet of particles. Quantum versions of this model are important in the context of the unitary Bose gas, which is currently under close theoretical and experimental scrutiny. In two dimensions, the three-body hard-core model possesses a conventional atomic liquid phase and a peculiar solid phase formed by dimers. These dimers interact effectively as hard disks. In three dimensions, the solid phase consists of isolated atoms that arrange in a simple-hexagonal lattice. Copyright (C) EPLA, 2015
Two-Dimensional Melting: From Liquid-Hexatic Coexistence to Continuous Transitions - Kapfer, Sebastian C. and Krauth, Werner
PHYSICAL REVIEW LETTERS 114 (2015) 
LPS


Abstract : The phase diagram of two-dimensional continuous particle systems is studied using the event-chain Monte Carlo algorithm. For soft disks with repulsive power-law interactions proportional to r(-n) with n greater than or similar to 6, the recently established hard-disk melting scenario (n -> infinity) holds: a first-order liquid-hexatic and a continuous hexatic-solid transition are identified. Close to n = 6, the coexisting liquid exhibits very long orientational correlations, and positional correlations in the hexatic are extremely short. For n less than or similar to 6, the liquid-hexatic transition is continuous, with correlations consistent with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario. To illustrate the generality of these results, we demonstrate that Yukawa particles likewise may follow either the KTHNYor the hard-disk melting scenario, depending on the Debye-Huckel screening length as well as on the temperature.
Hard-sphere melting and crystallization with event-chain Monte Carlo - Isobe, Masaharu and Krauth, Werner
JOURNAL OF CHEMICAL PHYSICS 143 (2015) 
LPS


Abstract : We simulate crystallization and melting with local Monte Carlo (LMC), with event-chain Monte Carlo (ECMC), and with event-driven molecular dynamics (EDMD) in systems with up to one million three-dimensional hard spheres. We illustrate that our implementations of the three algorithms rigorously coincide in their equilibrium properties. We then study nucleation in the NVE ensemble from the fcc crystal into the homogeneous liquid phase and from the liquid into the homogeneous crystal. ECMC and EDMD both approach equilibrium orders of magnitude faster than LMC. ECMC is also notably faster than EDMD, especially for the equilibration into a crystal from a disordered initial condition at high density. ECMC can be trivially implemented for hard-sphere and for soft-sphere potentials, and we suggest possible applications of this algorithm for studying jamming and the physics of glasses, as well as disordered systems. (C) 2015 AIP Publishing LLC.
Event-chain Monte Carlo for classical continuous spin models - Michel, Manon and Mayer, Johannes and Krauth, Werner
EPL 112 (2015) 
LPS


Abstract : We apply the event-chain Monte Carlo algorithm to classical continuum spin models on a lattice and clarify the condition for its validity. In the two-dimensional XY model, it outperforms the local Monte Carlo algorithm by two orders of magnitude, although it remains slower than the Wolff cluster algorithm. In the three-dimensional XY spin glass model at low temperature, the event-chain algorithm is far superior to the other algorithms. Copyright (C) EPLA, 2015
Event-chain algorithm for the Heisenberg model: Evidence for z similar or equal to 1 dynamic scaling - Nishikawa, Yoshihiko and Michel, Manon and Krauth, Werner and Hukushima, Koji
PHYSICAL REVIEW E 92 (2015) 
LPS


Abstract : We apply the event-chain Monte Carlo algorithm to the three-dimensional ferromagnetic Heisenberg model. The algorithm is rejection-free and also realizes an irreversible Markov chain that satisfies global balance. The autocorrelation functions of the magnetic susceptibility and the energy indicate a dynamical critical exponent z approximate to 1 at the critical temperature, while that of the magnetization does not measure the performance of the algorithm. We show that the event-chain Monte Carlo algorithm substantially reduces the dynamical critical exponent from the conventional value of z similar or equal to 2.
 
2014
Generalized event-chain Monte Carlo: Constructing rejection-free global-balance algorithms from infinitesimal steps - Michel, Manon and Kapfer, Sebastian C. and Krauth, Werner
JOURNAL OF CHEMICAL PHYSICS 140 (2014) 
LPS


Abstract : In this article, we present an event-driven algorithm that generalizes the recent hard-sphere event-chain Monte Carlo method without introducing discretizations in time or in space. A factorization of the Metropolis filter and the concept of infinitesimal Monte Carlo moves are used to design a rejection-free Markov-chain Monte Carlo algorithm for particle systems with arbitrary pairwise interactions. The algorithm breaks detailed balance, but satisfies maximal global balance and performs better than the classic, local Metropolis algorithm in large systems. The new algorithm generates a continuum of samples of the stationary probability density. This allows us to compute the pressure and stress tensor as a byproduct of the simulation without any additional computations. (C) 2014 AIP Publishing LLC.
Efimov-driven phase transitions of the unitary Bose gas - Piatecki, Swann and Krauth, Werner
NATURE COMMUNICATIONS 5 (2014) 
LPS


Abstract : Initially predicted in nuclear physics, Efimov trimers are bound configurations of three quantum particles that fall apart when any one of them is removed. They open a window into a rich quantum world that has become the focus of intense experimental and theoretical research, as the region of `unitary' interactions, where Efimov trimers form, is now accessible in cold-atom experiments. Here we use a path-integral Monte Carlo algorithm backed up by theoretical arguments to show that unitary bosons undergo a first-order phase transition from a normal gas to a superfluid Efimov liquid, bound by the same effects as Efimov trimers. A triple point separates these two phases and another superfluid phase, the conventional Bose-Einstein condensate, whose coexistence line with the Efimov liquid ends in a critical point. We discuss the prospects of observing the proposed phase transitions in cold-atom systems.
 
2013
DOI
10
Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods - Engel, Michael and Anderson, Joshua A. and Glotzer, Sharon C. and Isobe, Masaharu and Bernard, Etienne P. and Krauth, Werner
PHYSICAL REVIEW E 87 (2013) 
LPS


Abstract : We report large-scale computer simulations of the hard-disk system at high densities in the region of the melting transition. Our simulations reproduce the equation of state, previously obtained using the event-chain Monte Carlo algorithm, with a massively parallel implementation of the local Monte Carlo method and with event-driven molecular dynamics. We analyze the relative performance of these simulation methods to sample configuration space and approach equilibrium. Our results confirm the first-order nature of the melting phase transition in hard disks. Phase coexistence is visualized for individual configurations via the orientational order parameter field. The analysis of positional order confirms the existence of the hexatic phase.
 
2012
DOI
11
Event-chain Monte Carlo algorithms for hard-sphere systems (vol 80, 056704, 2009) - Bernard, Etienne P. and Krauth, Werner
PHYSICAL REVIEW E 86 (2012) 
LPS


Abstract : We extend the event-chain Monte Carlo algorithm from hard-sphere interactions to general potentials. This event-driven Monte Carlo algorithm is nonlocal and rejection free and allows for the breaking of detailed balance. The algorithm uses a discretized potential, but its running speed is asymptotically independent of the discretization. We apply the algorithm to two-dimensional soft spheres and discuss its possible implementation directly in the continuum limit.
 
2011
DOI
12
Dynamics and Thermodynamics of the Low-Temperature Strongly Interacting Bose Gas - Navon, Nir and Piatecki, Swann and Guenter, Kenneth and Rem, Benno and Trong Canh Nguyen and Chevy, Frederic and Krauth, Werner and Salomon, Christophe
PHYSICAL REVIEW LETTERS 107 (2011) 
LPS


Abstract : We measure the zero-temperature equation of state of a homogeneous Bose gas of Li-7 atoms by analyzing the in situ density distributions of trapped samples. For increasing repulsive interactions our data show a clear departure from mean-field theory and provide a quantitative test of the many-body corrections first predicted in 1957 by Lee, Huang, and Yang [Phys. Rev. 106, 1135 (1957).]. We further probe the dynamic response of the Bose gas to a varying interaction strength and compare it to simple theoretical models. We deduce a lower bound for the value of the universal constant xi > 0.44(8) that would characterize the universal Bose gas at the unitary limit.
DOI
13
Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition - Bernard, Etienne P. and Krauth, Werner
PHYSICAL REVIEW LETTERS 107 (2011) 
LPS


Abstract : Melting in two spatial dimensions, as realized in thin films or at interfaces, represents one of the most fascinating phase transitions in nature, but it remains poorly understood. Even for the fundamental hard-disk model, the melting mechanism has not been agreed upon after 50 years of studies. A recent Monte Carlo algorithm allows us to thermalize systems large enough to access the thermodynamic regime. We show that melting in hard disks proceeds in two steps with a liquid phase, a hexatic phase, and a solid. The hexatic-solid transition is continuous while, surprisingly, the liquid-hexatic transition is of first order. This melting scenario solves one of the fundamental statistical-physics models, which is at the root of a large body of theoretical, computational, and experimental research.
 
2010
DOI
14
Convergence and coupling for spin glasses and hard spheres - Chanal, Cedric and Krauth, Werner
PHYSICAL REVIEW E 81 (2010) 
LPS


Abstract : We discuss convergence and coupling of Markov chains, and present general relations between the transfer matrices describing these two processes. We then analyze a recently developed local-patch algorithm, which computes rigorous upper bound for the coupling time of a Markov chain for nontrivial statistical-mechanics models. Using the ``coupling from the past'' protocol, this allows one to exactly sample the underlying equilibrium distribution. For spin glasses in two and three spatial dimensions, the local-patch algorithm works at lower temperatures than previous exact-sampling methods. We discuss variants of the algorithm which might allow one to reach, in three dimensions, the spin-glass transition temperature. The algorithm can be adapted to hard-sphere models. For two-dimensional hard disks, the algorithm allows us to draw exact samples at higher densities than previously possible.
DOI
15
Universal correlations and coherence in quasi-two-dimensional trapped Bose gases - Holzmann, Markus and Chevallier, Maguelonne and Krauth, Werner
PHYSICAL REVIEW A 81 (2010) 
LPS


Abstract : We study the quasi-two-dimensional Bose gas in harmonic traps at temperatures above the Kosterlitz-Thouless transition, where the gas is in the normal phase. We show that mean-field theory takes into account the dominant interaction effects for experimentally relevant trap geometries. Comparing with quantum Monte Carlo calculations, we quantify the onset of the fluctuation regime, where correlations beyond mean-field become important. Although the density profile depends on the microscopic parameters of the system, we show that the correlation density (the difference between the exact and the mean-field density) is accurately described by a universal expression, obtained from classical-field calculations of the homogeneous strictly two-dimensional gas. Deviations from universality, due to the finite value of the interaction or to the trap geometry, are shown to be small for current experiments. We further study coherence and pair correlations on a microscopic scale. Finite-size effects in the off-diagonal density matrix allow us to characterize the crossover from Kosterlitz-Thouless to Bose-Einstein behavior for small particle numbers. Bose-Einstein condensation occurs below a characteristic number of particles which rapidly diverges with vanishing interactions.
DOI
16
Equilibrium state of a trapped two-dimensional Bose gas - Rath, Steffen P. and Yefsah, Tarik and Guenter, Kenneth J. and Cheneau, Marc and Desbuquois, Remi and Holzmann, Markus and Krauth, Werner and Dalibard, Jean
PHYSICAL REVIEW A 82 (2010) 
LPS


Abstract : We study experimentally and numerically the equilibrium density profiles of a trapped two-dimensional (87)Rb Bose gas and investigate the equation of state of the homogeneous system using the local density approximation. We find a clear discrepancy between in situ measurements and quantum Monte Carlo simulations, which we attribute to a nonlinear variation of the optical density of the atomic cloud with its spatial density. However, good agreement between experiment and theory is recovered for the density profiles measured after time of flight, taking advantage of their self-similarity in a two-dimensional expansion.
DOI
17
Damage spreading and coupling in Markov chains - Bernard, Etienne P. and Chanal, Cedric and Krauth, Werner
EPL 92 (2010) 
LPS


Abstract : In this paper, we relate the coupling of Markov chains, at the basis of perfect sampling methods, with damage spreading, which captures the chaotic nature of stochastic dynamics. For two-dimensional spin glasses and hard spheres we point out that the obstacle to the application of perfect-sampling schemes is posed by damage spreading rather than by the survey problem of the entire configuration space. We find dynamical damage-spreading transitions deeply inside the paramagnetic and liquid phases, and we show that the critical values of the transition temperatures and densities depend on the coupling scheme. We discuss our findings in the light of a classic proof that for arbitrary Monte Carlo algorithms damage spreading can be avoided through non-Markovian coupling schemes. Copyright (C) EPLA, 2010
 
2009
DOI
18
Thermal effects in the dynamics of disordered elastic systems - Bustingorry, S. and Kolton, A. B. and Rosso, A. and Krauth, W. and Giamarchi, T.
PHYSICA B-CONDENSED MATTER 404444-446 (2009) 
LPS


Abstract : Many seemingly different macroscopic systems (magnets, ferroelectrics, CDW, vortices, etc.) can be described as generic disordered elastic systems. Understanding their static and dynamics thus poses challenging problems both from the point of view of fundamental physics and of practical applications. Despite important progress many questions remain open. In particular the temperature has drastic effects on the way these systems respond to an external force. We address here the important question of the thermal effect close to depinning, and whether these effects can be understood in the analogy with standard critical phenomena, analogy so useful to understand the zero temperature case. We show that close to the depinning force temperature leads to a rounding of the depinning transition and compute the corresponding exponent. In addition, using a novel algorithm it is possible to study precisely the behavior close to depinning, and to show that the commonly accepted analogy of the depinning with a critical phenomenon does not fully hold, since no divergent lengthscale exists in the steady state properties of the line below the depinning threshold. (c) 2008 Elsevier B.V. All rights reserved.
DOI
19
Event-chain Monte Carlo algorithms for hard-sphere systems - Bernard, Etienne P. and Krauth, Werner and Wilson, David B.
PHYSICAL REVIEW E 80 (2009) 
LPS


Abstract : In this paper we present the event-chain algorithms, which are fast Markov-chain Monte Carlo methods for hard spheres and related systems. In a single move of these rejection-free methods, an arbitrarily long chain of particles is displaced, and long-range coherent motion can be induced. Numerical simulations show that event-chain algorithms clearly outperform the conventional Metropolis method. Irreversible versions of the algorithms, which violate detailed balance, improve the speed of the method even further. We also compare our method with a recent implementations of the molecular-dynamics algorithm.
 
2008
DOI
20
Renormalization group approach to exact sampling - Chanal, Cedric and Krauth, Werner
PHYSICAL REVIEW LETTERS 100 (2008) 
LPS


Abstract : In this Letter, we use a general renormalization-group algorithm to implement Propp and Wilson's ``coupling from the past'' approach to complex physical systems. Our algorithm follows the evolution of the entire configuration space under the Markov chain Monte Carlo dynamics from parts of the configurations (patches) on increasing length scales, and it allows us to generate ``exact samples'' of the Boltzmann distribution, which are rigorously proven to be uncorrelated with the initial condition. We validate our approach in the two-dimensional Ising spin glass on lattices of size 64 x 64.