class Simulation:
# Seed random number generator: self.rng() will give a random float from the interval [0,1)
rng = alpstools.rng(42)
def __init__(self, beta, L):
self.L = L
self.beta = beta
# Init exponential map
self.exp_table = dict()
for E in range(-4, 5, 2):
self.exp_table[E] = math.exp(2 * beta * E)
# Init random spin configuration
self.spins = [[2 * self.randint(2) - 1 for j in range(L)]
for i in range(L)]
# Init observables
self.energy = alpsalea.RealObservable('E')
self.magnetization = alpsalea.RealObservable('m')
self.abs_magnetization = alpsalea.RealObservable('|m|')
def save(self, filename):
pyalps.save_parameters(
filename, {
'L': self.L,
'BETA': self.beta,
'SWEEPS': self.n,
'THERMALIZATION': self.ntherm
})
self.abs_magnetization.save(filename)
self.energy.save(filename)
self.magnetization.save(filename)
def run(self, ntherm, n):
# Thermalize for ntherm steps
self.n = n
self.ntherm = ntherm
while ntherm > 0:
self.step()
ntherm = ntherm - 1
# Run n steps
while n > 0:
self.step()
self.measure()
n = n - 1
# Print observables
print '|m|:\t', self.abs_magnetization.mean, '+-', self.abs_magnetization.error, ',\t tau =', self.abs_magnetization.tau
print 'E:\t', self.energy.mean, '+-', self.energy.error, ',\t tau =', self.energy.tau
print 'm:\t', self.magnetization.mean, '+-', self.magnetization.error, ',\t tau =', self.magnetization.tau
def step(self):
for s in range(self.L * self.L):
# Pick random site k=(i,j)
...
# Measure local energy e = -s_k * sum_{l nn k} s_l
...
# Flip s_k with probability exp(2 beta e)
...
def measure(self):
E = 0. # energy
M = 0. # magnetization
for i in range(self.L):
for j in range(self.L):
E -=...
M +=...
# Add sample to observables
self.energy << E / (self.L * self.L)
self.magnetization << M / (self.L * self.L)
self.abs_magnetization << abs(M) / (self.L * self.L)
# Random int from the interval [0,max)
def randint(self, max):
return int(max * self.rng())
class Simulation:
# Seed random number generator: self.rng() will give a random float from the interval [0,1)
rng = alpstools.rng(42)
def __init__(self,beta,L):
self.L = L
self.beta = beta
# Init exponential map
self.exp_table = dict()
for E in range(-8,10,4):
self.exp_table[E] = math.exp(2*beta*E)
#self.exp_table[E] = math.exp(-beta*E) #math.exp(beta*E)
# Init random spin configuration
self.spins = [ [2*self.randint(2)-1 for j in range(L)] for i in range(L) ]
# Init observables
self.energy = alpsalea.RealObservable('E')
self.magnetization = alpsalea.RealObservable('m')
self.abs_magnetization = alpsalea.RealObservable('|m|')
self.magnetization_2 = alpsalea.RealObservable('m^2')
self.magnetization_4 = alpsalea.RealObservable('m^4')
self.accepted = 0
def save(self, filename):
pyalps.save_parameters(filename, {'L':self.L, 'BETA':self.beta, 'SWEEPS':self.n, 'THERMALIZATION':self.ntherm})
self.abs_magnetization.save(filename)
self.energy.save(filename)
self.magnetization.save(filename)
self.magnetization_2.save(filename)
self.magnetization_4.save(filename)
def run(self,ntherm,n):
# Thermalize for ntherm steps
self.n = n
self.ntherm = ntherm
while ntherm > 0:
self.step()
ntherm = ntherm-1
# Run n steps
while n > 0:
self.step()
self.measure()
n = n-1
# Print observables
print '|m|:\t', self.abs_magnetization.mean, '+-', self.abs_magnetization.error, ',\t tau =', self.abs_magnetization.tau
print 'E:\t', self.energy.mean, '+-', self.energy.error, ',\t tau =', self.energy.tau
print 'm:\t', self.magnetization.mean, '+-', self.magnetization.error, ',\t tau =', self.magnetization.tau
def energyLocal(self, spin, i, j):
e = self.spins[(i-1+self.L)%self.L][j] + self.spins[(i+1)%self.L][j] + self.spins[i][(j-1+self.L)%self.L] + self.spins[i][(j+1)%self.L]
e *= -spin
return e
def step(self):
for s in range(self.L*self.L):
# Pick random site k=(i,j)
i = self.randint(self.L)
j = self.randint(self.L)
newSpin = -self.spins[i][j]
de = self.energyLocal(newSpin, i, j) - self.energyLocal(self.spins[i][j], i, j)
#de = self.deltaEnergy(i, j)
# Flip s_k with probability exp(2 beta e)
#if e > 0 or self.rng() < self.exp_table[e]:
# self.spins[i][j] = -self.spins[i][j]
if de < 0 or self.rng() < math.exp(-self.beta*de): #de<=0 breaks the binder plot ...
self.spins[i][j] = newSpin
self.accepted += 1
def measure(self):
E = 0. # energy
M = 0. # magnetization
for i in range(self.L):
for j in range(self.L):
E -= self.spins[i][j] * (self.spins[(i+1)%self.L][j] + self.spins[i][(j+1)%self.L])
M += self.spins[i][j]
# Add sample to observables
self.energy << E/(self.L*self.L)
self.magnetization << M/(self.L*self.L)
self.abs_magnetization << abs(M)/(self.L*self.L)
self.magnetization_2 << (M/(self.L*self.L))*(M/(self.L*self.L))
self.magnetization_4 << (M/(self.L*self.L))*(M/(self.L*self.L))*(M/(self.L*self.L))*(M/(self.L*self.L))
# Random int from the interval [0,max)
def randint(self,max):
return int(max*self.rng())
class Simulation:
# Seed random number generator: self.rng() will give a random float from the interval [0,1)
rng = alpstools.rng(42)
def __init__(self, beta, L, model=None):
# Init size and temp
self.L = L
self.beta = beta
# Init random spin configuration
self.spins = [[
spin.Spin(sx=0.0, sy=0.0, sz=2 * self.randint(2) - 1)
for j in range(L)
] for i in range(L)]
# Init observables
self.energy = alpsalea.RealObservable('E')
self.magnetization = alpsalea.RealObservable('m')
self.abs_magnetization = alpsalea.RealObservable('|m|')
self.magnetization_2 = alpsalea.RealObservable('m^2')
self.magnetization_4 = alpsalea.RealObservable('m^4')
self.accepted = 0
#==============================================================================
# HAMILTONIANS
#==============================================================================
def isingH(spin, i, j):
e = self.spins[(i-1+self.L)%self.L][j].sz +\
self.spins[(i+1)%self.L][j].sz +\
self.spins[i][(j-1+self.L)%self.L].sz +\
self.spins[i][(j+1)%self.L].sz
e *= -spin.sz
return e
def antiIsingH(spin, i, j):
e = self.spins[(i-1+self.L)%self.L][j].sz +\
self.spins[(i+1)%self.L][j].sz +\
self.spins[i][(j-1+self.L)%self.L].sz +\
self.spins[i][(j+1)%self.L].sz
e *= spin.sz
return e
# currently not long-range.
def dipoledipoleH(spin, i, j):
rCutOff = 3
e = 0
for dx in range(-1, 2, 2):
for dy in range(-1, 2, 2):
if (dx * dx + dy * dy >
rCutOff * rCutOff): #hard code for now.
r = math.sqrt(dx * dx + dy * dy)
rvec = spin.Spin(sx=dx, sy=dy, sz=0.0)
e += self.spins[i][j].dot(
self.spins[(i + dx) % self.L][(j + dy) % self.L])
e += (self.spins[i][j].dot(rvec)) * (self.spins[
(i + dx) % self.L][(j + dy) % self.L].dot(rvec))
e *= 1.0 / (r * r * r)
return e
#==============================================================================
# SPIN MOVE / FLIP TYPES
#==============================================================================
def flip180(spinToFlip):
return spin.Spin(sx=spinToFlip.sx,
sy=spinToFlip.sy,
sz=-spinToFlip.sz)
self.Potts6LookUp = [[0, 0, 1], [0, 0, -1], [0, 1, 0], [0, -1, 0],
[1, 0, 0], [-1, 0, 0]]
def flipPotts6(spinToFlip):
whichVector = self.randint(len(self.Potts6LookUp))
sx = self.Potts6LookUp[whichVector][0]
sy = self.Potts6LookUp[whichVector][1]
sz = self.Potts6LookUp[whichVector][2]
return spin.Spin(sx=sx, sy=sy, sz=sz)
if model == 'Ising':
self.energyLocal = isingH
self.flip = flip180
elif model == 'AntiFerroIsing':
self.energyLocal = antiIsingH
self.flip = flip180
elif model == 'dipole-dipole6':
self.energyLocal = dipoledipoleH
self.flip = flipPotts6
def save(self, filename):
pyalps.save_parameters(
filename, {
'L': self.L,
'BETA': self.beta,
'SWEEPS': self.n,
'THERMALIZATION': self.ntherm
})
self.abs_magnetization.save(filename)
self.energy.save(filename)
self.magnetization.save(filename)
self.magnetization_2.save(filename)
self.magnetization_4.save(filename)
def run(self, ntherm, n):
# Thermalize for ntherm steps
self.n = n
self.ntherm = ntherm
while ntherm > 0:
self.step()
ntherm = ntherm - 1
# Run n steps
while n > 0:
self.step()
self.measure()
n = n - 1
# Print observables
print '|m|:\t', self.abs_magnetization.mean, '+-', self.abs_magnetization.error, ',\t tau =', self.abs_magnetization.tau
print 'E:\t', self.energy.mean, '+-', self.energy.error, ',\t tau =', self.energy.tau
print 'm:\t', self.magnetization.mean, '+-', self.magnetization.error, ',\t tau =', self.magnetization.tau
def step(self):
for s in range(self.L * self.L):
# Pick random site k=(i,j)
i = self.randint(self.L)
j = self.randint(self.L)
newSpin = self.flip(self.spins[i][j])
de = self.energyLocal(newSpin, i, j) - self.energyLocal(
self.spins[i][j], i, j)
#de = self.deltaEnergy(i, j)
# Flip s_k with probability exp(2 beta e)
#if e > 0 or self.rng() < self.exp_table[e]:
# self.spins[i][j] = -self.spins[i][j]
if de < 0 or self.rng() < math.exp(
-self.beta * de): #de<=0 breaks the binder plot ...
self.spins[i][j] = newSpin
self.accepted += 1
def measure(self):
E = 0. # energy
M = 0. # magnetization
for i in range(self.L):
for j in range(self.L):
E -= self.spins[i][j].sz * (self.spins[
(i + 1) % self.L][j].sz +
self.spins[i][(j + 1) % self.L].sz)
M += self.spins[i][j].sz
# Add sample to observables
self.energy << E / (self.L * self.L)
self.magnetization << M / (self.L * self.L)
self.abs_magnetization << abs(M) / (self.L * self.L)
self.magnetization_2 << (M / (self.L * self.L)) * (M /
(self.L * self.L))
self.magnetization_4 << (M / (self.L * self.L)) * (
M / (self.L * self.L)) * (M /
(self.L * self.L)) * (M /
(self.L * self.L))
def spinsToFile(self, outputFile):
if outputFile is None:
raise TypeError("Please supply an output file name!")
else:
f = open(outputFile, 'w')
for i in range(self.L):
for j in range(self.L):
f.write(str(i)+','+str(j)+','+\
str(self.spins[i][j].sx)+','+\
str(self.spins[i][j].sy)+','+\
str(self.spins[i][j].sz)+'\n')
f.close()
print 'saved spins to ' + str(outputFile)
# Random int from the interval [0,max)
def randint(self, max):
return int(max * self.rng())