From Werner KRAUTH

Revision as of 21:39, 22 September 2015 Werner (Talk | contribs) ← Previous diff		Current revision Werner (Talk | contribs)
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-	This page presents the program markov_disks_box.py, a Markov-chain algorithm for four disks in a square box of sides 1.	+	This page presents the Python3 program enumerate_ising.py, an enumeration algorithm for the Ising model using the Gray code, on the two-dimensional L x L lattice with periodic boundary conditions. As it stands, the program is only really suited for L=2 and L=4. As Python is a bit slow, it will take a few hours to terminate for L=6.
	__FORCETOC__		__FORCETOC__
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	=Program=		=Program=
-
-	import random
-
-	L = [[0.25, 0.25], [0.75, 0.25], [0.25, 0.75], [0.75, 0.75]]
-	sigma = 0.15
-	sigma_sq = sigma ** 2
-	delta = 0.1
-	n_steps = 1000
-	for steps in range(n_steps):
-	a = random.choice(L)
-	b = [a[0] + random.uniform(-delta, delta), a[1] + random.uniform(-delta, delta)]
-	min_dist = min((b[0] - c[0]) ** 2 + (b[1] - c[1]) ** 2 for c in L if c != a)
-	box_cond = min(b[0], b[1]) < sigma or max(b[0], b[1]) > 1.0 - sigma
-	if not (box_cond or min_dist < 4.0 * sigma ** 2):
-	a[:] = b
-	print L
-
-	=Version=
-	See history for version information.
-
-	[[Category:Python]]
-
-
	def gray_flip(t, N):		def gray_flip(t, N):
	k = t[0]		k = t[0]
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	E += 2 * h * S[k - 1]		E += 2 * h * S[k - 1]
	S[k - 1] *= -1		S[k - 1] *= -1
-	print S, E	+	print(S, E)
		+
		+	=Version=
		+	See history for version information.
		+
		+	[[Category:Python]] [[Category:Oxford_2024]] [[Category:MOOC_SMAC]]

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Current revision

This page presents the Python3 program enumerate_ising.py, an enumeration algorithm for the Ising model using the Gray code, on the two-dimensional L x L lattice with periodic boundary conditions. As it stands, the program is only really suited for L=2 and L=4. As Python is a bit slow, it will take a few hours to terminate for L=6.

Contents 1 Description 2 Program 3 Version

Description

Program

def gray_flip(t, N):
    k = t[0]
    if k > N: return t, k
    t[k - 1] = t[k]
    t[k] = k + 1
    if k != 1: t[0] = 1
    return t, k

L = 4
N = L * L
nbr = {i : ((i // L) * L + (i + 1) % L, (i + L) % N,
            (i // L) * L + (i - 1) % L, (i - L) % N)
                                    for i in range(N)}
S = [-1] * N
E = -2 * N
print S, E
tau = range(1, N + 2)
for i in range(1, 2 ** N):
    tau, k = gray_flip(tau, N)
    h = sum(S[n] for n in nbr[k - 1])
    E += 2 * h * S[k - 1]
    S[k - 1] *= -1
    print(S, E)

Version

See history for version information.