def main():
l=15
h=0.1
j=1
n_configs = 250
n_usable_configs = 200
temps = numpy.linspace(10,0.5,40)
magnetism = numpy.zeros((len(temps),1))
previous_lattice = [[round(random())*2 -1 for x in range(l)] for y in range(l)]
previous_lattice = numpy.array(previous_lattice)
for index, temp in enumerate(temps):
print(temp)
lattice = create_lattice(l,h,j,previous_lattice, n_configs, n_usable_configs, temp)
mag = numpy.sum(lattice)/(l**2)
magnetism[index] = mag/n_usable_configs
#q4
mag = numpy.mean(mag**2)
susceptibility[index] = (mag - mean(mag)**2)/(temp**2)
previous_lattice = lattice[:,:,-1]
plotly.offline.plot({
"data": [Scatter(x=temps,y=magnetism, mode="markers")],
"layout": Layout(title="Magnetism")
}, filename="q3.html")
plotly.offline.plot({
"data": [Scatter(x=temps, y=susceptibility, mode="markers")],
"layout": Layout(title="Susceptibility")
}, filename="q4.html")
def main():
l = 15
h = 0.1
j = 1
n_configs = 250
n_usable_configs = 200
temps = numpy.linspace(10, .5, 20)
specific_heat = numpy.zeros((len(temps), 1))
stable_spins = numpy.zeros((len(temps),1))
previous_lattice = [[round(random()) * 2 -1 for x in range(l)] for y in range(l)]
previous_lattice = numpy.array(previous_lattice)
for index, temp in enumerate(temps):
print(temp)
lattice = create_lattice(l,h,j, previous_lattice, n_configs, n_usable_configs, temp)
lattice_pad = numpy.zeros((l+2, l+2, n_usable_configs))
for config in range(n_usable_configs):
lattice_pad[:,:,config] = pad(lattice[:,:,config])
end_x = lattice_pad.shape[0]-1
end_y = lattice_pad.shape[1]-1
north = lattice_pad[0:end_x-1,1:end_y,:]
south = lattice_pad[2:end_x+1,1:end_y,:]
east = lattice_pad[1:end_x,2:end_y+1,:]
west = lattice_pad[1:end_x,0:end_y-1,:]
f = -1 * h * numpy.sum(lattice)
s = -1 * j/2 * numpy.sum(lattice *
(north + south + east + west))
energy = (f+s)/n_usable_configs
heat = (energy**2/n_usable_configs - energy**2)/(temp**2)
specific_heat[index] = heat
#q5
spin = (lattice==north) & (lattice==south) & (lattice==east) & (lattice==west)
stable_spins[index] = numpy.sum(spin)/n_usable_configs
previous_lattice = lattice[:,:,-1]
plotly.offline.plot({
"data": [ Scatter(x=temps, y=specific_heat, mode="markers") ],
"layout": Layout(title="Specific Heat")
}, filename="q2.html")
fitted_line = scipy.stats.powerlaw.fit(stable_spins)
power_eq = scipy.stats(power_eq)
power_law = [power_eq(x) for x in temps]
plotly.offline.plot({
"data": [ Scatter(x=temps, y=stable_spins, mode="markers"),
Scatter(x=temps, y=power_law, mode="lines")],
"layout": Layout(title="Stable Spins")
}, filename="q5.html")
def main():
l = 15
h = 0.1
j = 1
n_configs = 250
n_usable_configs = 200
temps = numpy.linspace(10,.5,20)
energy = numpy.zeros((len(temps), 1))
initial_energy = numpy.ones((l, l))
last_lattice = initial_energy
for iTemp, temp in enumerate(temps):
print(temp)
lattice = create_lattice(l, h, j, last_lattice, n_configs, n_usable_configs, temp)
lattice_pad = numpy.zeros((l+2, l+2, n_usable_configs))
for config in range(n_usable_configs):
lattice_pad[:,:,config] = pad(lattice[:,:,config])
end_x = lattice_pad.shape[0]-1
end_y = lattice_pad.shape[1]-1
north = lattice_pad[0:end_x-1,1:end_y,:]
south = lattice_pad[2:end_x+1,1:end_y,:]
east = lattice_pad[1:end_x,2:end_y+1,:]
west = lattice_pad[1:end_x,0:end_y-1,:]
f = -1 * h * numpy.sum(lattice)
s = -1 * j/2 * numpy.sum(lattice *
(north + south + east + west))
energy_temp = (f+s)/n_usable_configs
energy[iTemp] = energy_temp
print("energy for ", temp, " = ", energy_temp)
last_lattice = lattice[:,:,-1]
print(energy)
plotly.offline.plot({
"data": [ Scatter(x=temps, y=energy, mode="markers") ],
"layout": Layout(title="Energy Consumption")
}, filename="q1.html")