def monte_carlo_ising( (L, T, num_sweeps) ):
V = L*L
beta = 1.0/T
# generate random configuration
sigma = random.randint(0, 2, (L, L))
sigma *= 2
sigma -= 1
E = compute_energy(sigma)
mu = sigma.sum()
Es = empty(num_sweeps, int)
ms = empty(num_sweeps, int)
mc.core(E, mu, Es, ms, num_sweeps, sigma, beta)
Es = Es/float(V)
ms = abs(ms)/float(V)
Emean, _, Eerr, tauE, _, _, _, _ = compute_act_error(Es)
mmean, _, merr, tauM, _, _, _, _ = compute_act_error(ms)
print "\rT = {} tau_E = {} tau_M = {} E = {}+/-{} m = {}+/-{}"\
.format(T, tauE, tauM, Emean, Eerr, mmean, merr)
return Emean, Eerr, mmean, merr, sigma, Es, ms
def exact_sum(L, Ts):
# we compute the mean energy and magnetization for all
# temperatures at once!
ws = zeros_like(Ts)
Es = zeros_like(Ts)
ms = zeros_like(Ts)
# beta is a NumPy array with len(Ts) elements
beta = 1./Ts
V = float(L*L)
sigma = ones((L, L), dtype=int)
# the bit pattern of the integer "state" is used to generate all
# possible states of sigma
for state in range(2**(L*L)):
# read out the bitpattern
for i in range(L):
for j in range(L):
k = i*L + j
if state & 2**k > 0:
sigma[i,j] = 1
else:
sigma[i,j] = -1
# compute energy and magnetization of this state
E = compute_energy(sigma)
mu = compute_magnetization(sigma)
# this is a vector operation, as beta is a vector
w = exp(-beta*E)
ws += w
Es += E/V*w
ms += abs(mu)/V*w
Emeans = Es/ws
mmeans = ms/ws
return Emeans, mmeans