def test_z():
for T in np.linspace(1., 10., 5):
analytic = a.z(T)
calculated = 0
states = a.produce_states()
for state in states:
energy = a.energy(state)
calculated += np.exp(-1 / T * energy)
assert analytic == approx(calculated, abs=tol)
def test_expected_energy():
"<E>"
for T in np.linspace(1., 10., 5):
analytic = a.expected_energy(T)
states = a.produce_states()
calculated = 0
for state in states:
energy = a.energy(state)
prob = a.probability(T, state)
calculated += prob * energy
assert analytic == approx(calculated, abs=tol)
def test_E2():
"<E^2>"
for T in np.linspace(1., 10., 5):
B = 1 / T
analytic = 256 / a.z(T) * np.cosh(8 * B)
states = a.produce_states()
calculated = 0
for state in states:
energy = a.energy(state)
prob = a.probability(T, state)
calculated += prob * energy**2
assert analytic == approx(calculated, abs=tol)
def test_variance_magnetization():
for T in np.linspace(1., 10., 5):
analytic = a.variance_magnetization(T)
states = a.produce_states()
M2 = 0
M = 0
for state in states:
magnetization = np.abs(a.magnetization(state))
prob = a.probability(T, state)
M2 += magnetization**2 * prob
M += magnetization * prob
assert analytic == approx(M2 - M**2, abs=tol)
def test_Esquared():
"<E>^2"
for T in np.linspace(1., 10., 3):
B = 1 / T
zt = a.z(T)
analytic = 32**2 / (zt)**2 * np.sinh(8 * B)**2
states = a.produce_states()
calculated = 0
for state in states:
energy = a.energy(state)
prob = a.probability(T, state)
calculated += prob * energy
assert analytic == approx(calculated**2)
def test_Msquared():
"""
<M>^2
"""
for T in np.linspace(1., 10., 5):
B = 1 / T
analytic = 64 / a.z(T)**2 * (4 * np.exp(8 * B) + np.exp(16 * B) + 4)
states = a.produce_states()
calculated = 0
for state in states:
magnet = np.abs(a.magnetization(state))
prob = a.probability(T, state)
calculated += prob * magnet
assert analytic == approx(calculated**2, abs=tol)
def test_M2():
"""
<M^2>
"""
for T in np.linspace(1., 10., 5):
B = 1 / T
analytic = 32 / a.z(T) * (np.exp(8 * B) + 1)
states = a.produce_states()
calculated = 0
for state in states:
magnet = np.abs(a.magnetization(state))
prob = a.probability(T, state)
calculated += prob * magnet**2
assert analytic == approx(calculated, abs=tol)
def test_variance_energy():
for T in np.linspace(1., 10., 5):
T = 1.
B = 1 / T
analytic = a.variance_energy(T)
states = a.produce_states()
E2 = 0
E = 0
for state in states:
energy = a.energy(state)
prob = a.probability(T, state)
E2 += energy**2 * prob
E += energy * prob
assert analytic == approx(E2 - E**2, abs=tol)
def test_M():
"""
<M>
"""
for T in np.linspace(1., 10., 5):
# analytic = a.expected_magnetization(T)
zt = a.z(T)
B = 1 / T
analytic = 8 / zt * (np.exp(8 * B) + 2)
states = a.produce_states()
calculated = 0
for state in states:
magnetization = a.magnetization(state)
prob = a.probability(T, state)
calculated += np.abs(magnetization) * prob
assert analytic == approx(calculated, abs=tol)
