Combinatorial ising.py
From Werner KRAUTH
(Difference between revisions)
| Revision as of 19:49, 19 October 2015 Werner (Talk | contribs) ← Previous diff |
Revision as of 19:50, 19 October 2015 Werner (Talk | contribs) Next diff → |
||
| Line 3: | Line 3: | ||
| __FORCETOC__ | __FORCETOC__ | ||
| =Reference= | =Reference= | ||
| - | [[Krauth_2006|W. Krauth ''Statistical Mechanics: Algorithms and Computations'' Oxford University Press (2006)]] | + | [[SMAC|W. Krauth ''Statistical Mechanics: Algorithms and Computations'' Oxford University Press (2006)]] |
| =Description= | =Description= | ||
| This is a Python implementation of the Kac-Ward matrix that allows to compute the partition function of the two-dimensional Ising model without periodic boundary conditions. | This is a Python implementation of the Kac-Ward matrix that allows to compute the partition function of the two-dimensional Ising model without periodic boundary conditions. | ||
Revision as of 19:50, 19 October 2015
This page presents the program combinatorial_ising.py, naively implemented for the 2x2 lattice and the 4x4 lattice
Contents |
Reference
W. Krauth Statistical Mechanics: Algorithms and Computations Oxford University Press (2006)
Description
This is a Python implementation of the Kac-Ward matrix that allows to compute the partition function of the two-dimensional Ising model without periodic boundary conditions.
Program
alphabar = numpy.exp(-comp_i * math.pi / 4.0) * math.tanh(beta)
# 4x4 matrices 'right', 'up', 'left', 'down', 'one', 'zero'
r = numpy.mat([ [nu, alpha, 0.0, alphabar], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]], dtype=complex)
u = numpy.mat([ [0.0, 0.0, 0.0, 0.0], [alphabar, nu, alpha, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]], dtype=complex)
l = numpy.mat([ [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, alphabar, nu, alpha], [0.0, 0.0, 0.0, 0.0]], dtype=complex)
d = numpy.mat([ [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [alpha, 0.0, alphabar, nu]], dtype=complex)
o = numpy.mat([ [1.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 1.0]], dtype=complex)
z = numpy.mat([ [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]], dtype=complex)
U2x2 = numpy.bmat([ [o, r, u, z], [l, o, z, u], [d, z, o, r], [z, d, l, o]])
L = 2 n_edge = 2 * L * (L - 1) N = L ** 2
print 2 ** N * math.cosh(beta) ** n_edge * \ numpy.sqrt(numpy.real(numpy.linalg.det(U2x2))), ' Z_2x2 from Kac-Ward' print 2 ** 4 * math.cosh(beta) ** 4 * (1.0 + math.tanh(beta) ** 4), \ ' Z_2x2 from SMAC eq. (5.11)'
U4x4 = numpy.bmat([ #0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 [o, r, z, z, u, z, z, z, z, z, z, z, z, z, z, z], # line 0 [l, o, r, z, z, u, z, z, z, z, z, z, z, z, z, z], # line 1 [z, l, o, r, z, z, u, z, z, z, z, z, z, z, z, z], # line 2 [z, z, l, o, z, z, z, u, z, z, z, z, z, z, z, z], # line 3 [d, z, z, z, o, r, z, z, u, z, z, z, z, z, z, z], # line 4 [z, d, z, z, l, o, r, z, z, u, z, z, z, z, z, z], # line 5 [z, z, d, z, z, l, o, r, z, z, u, z, z, z, z, z], # line 6 [z, z, z, d, z, z, l, o, z, z, z, u, z, z, z, z], # line 7 [z, z, z, z, d, z, z, z, o, r, z, z, u, z, z, z], # line 8 [z, z, z, z, z, d, z, z, l, o, r, z, z, u, z, z], # line 9 [z, z, z, z, z, z, d, z, z, l, o, r, z, z, u, z], # line 10 [z, z, z, z, z, z, z, d, z, z, l, o, z, z, z, u], # line 11 [z, z, z, z, z, z, z, z, d, z, z, z, o, r, z, z], # line 12 [z, z, z, z, z, z, z, z, z, d, z, z, l, o, r, z], # line 13 [z, z, z, z, z, z, z, z, z, z, d, z, z, l, o, r], # line 14 [z, z, z, z, z, z, z, z, z, z, z, d, z, z, l, o]]) # line 15
L = 4 n_edge = 2 * L * (L - 1) N = L ** 2 print 2 ** N * math.cosh(beta) ** n_edge * \ math.sqrt(numpy.real(numpy.linalg.det(U4x4))), \ ' Z_4x4 from Kac-Ward' print 2 ** N * math.cosh(beta) ** n_edge * ( 1 + 9 * math.tanh(beta) ** 4 + 12 * math.tanh(beta) ** 6 + 50 * math.tanh(beta) ** 8 + 92 * math.tanh(beta) ** 10 + 158 * math.tanh(beta) ** 12 + 116 * math.tanh(beta) ** 14 + 69 * math.tanh(beta) ** 16 + 4 * math.tanh(beta) ** 18 + 1 * math.tanh(beta) ** 20), ' Z_4x4 from SMAC eq. (5.10)'
Version
See history for version information.
