def test_exch_1d():
"""
Test the x component of the exchange field
in a 1D mesh, with the spin ordering:
0 1 2 3 4 5
"""
mesh = CuboidMesh(nx=5, ny=1, nz=1)
sim = Sim(mesh)
exch = Exchange(1.0)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
assert field[0] == 1
assert field[1 * 3] == 2
assert field[2 * 3] == 4
assert field[3 * 3] == 6
assert field[4 * 3] == 3
assert np.max(field[2::3]) == 0
assert np.max(field[1::3]) == 0
def test_full_exch_hex_3_shells_lattice_pos():
"""
Test the x component of the exchange field when using 3 shells of
neighbours in a 9 x 9 hexagonal lattice with square arrangement
We set the s_x and s_y spin components as the (i, j) index of the
lattice positions:
"""
a = 1
shells = 3
mesh = HexagonalMesh(a * 0.5,
nx=9,
ny=9,
shells=shells,
alignment='square')
sim = Sim(mesh)
# Set the indexes (i, j) as their s_x, s_y position
sim.set_m(lambda r: init_m(r, a), normalise=False)
Js = np.ones(shells)
exch = Exchange(Js)
sim.add(exch)
field = exch.compute_field()
assert field[3 * 0] == (1 + 1 + 0) + (2 + 0) + (2 + 1) # f_x 1st spin
assert field[3 * 11] == ((3 + 1 + 2 + 1 + 1 + 2) +
(3 + 0 + 2 + 0 + 0 + 3) + (4 + 0 + 3 + 0 + 1 + 0))
def test_full_exch_hex_2_shells():
"""
Test the x component of the exchange field when using 2 shells of
neighbours, comparing the field manually.
This is similar than the *test_full_exch_hex_9_shells* function but
here we do not assume that the neighbours indexes are correct
We set J=1 for NN and J=2 for NNN
"""
a = 1
shells = 2
mesh = HexagonalMesh(a * 0.5,
nx=9,
ny=9,
shells=shells,
alignment='square')
sim = Sim(mesh)
sim.spin.reshape(-1, 3)[:,
0] = np.arange(len(sim.spin.reshape(-1, 3)[:, 0]))
Js = np.array([1., 2.])
exch = Exchange(Js)
sim.add(exch)
field = exch.compute_field()
assert field[3 * 0] == 1. * (1 + 10 + 9) + 2. * (11 + 18)
assert field[3 *
11] == (12 + 10 + 20 + 1 + 19 + 2) + 2. * (21 + 29 + 18 + 3)
def test_exch_1d():
"""
Test the x component of the exchange field
in a 1D mesh, with the spin ordering:
0 1 2 3 4 5
"""
mesh = CuboidMesh(nx=5, ny=1, nz=1)
sim = Sim(mesh)
exch = Exchange(1.0)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
assert field[0] == 1
assert field[1 * 3] == 2
assert field[2 * 3] == 4
assert field[3 * 3] == 6
assert field[4 * 3] == 3
assert np.max(field[2::3]) == 0
assert np.max(field[1::3]) == 0
def test_full_exch_hex_9_shells_J_rings():
"""
Test the x component of the exchange field when using 9 shells of
neighbours in a 11 X 11 hexagonal lattice with square and diagonal
arrangement
We set J=1,2,3,.. for every shell and set the s_x component of the spins as
the lattice site number:
[0, 1, 2, 3, ... 120]
Since we set the s_x components as the lattice position indexes, the x
component of the field is the sum of the indexes of the neighbours
(assuming the neighbours indexing is correct) multiplied by J[i] where i is
the shell (1, 2, ...9), i.e. the 1st shell of ngbs is multiplied by 1,
the 2nd shell by 2, the 3rd shell by 3, and so on
"""
for arrang in ['square', 'diagonal']:
a = 1
shells = 9
mesh = HexagonalMesh(a * 0.5,
nx=11,
ny=11,
shells=shells,
alignment=arrang)
sim = Sim(mesh)
# Set s_x as the lattice site number
sim.spin.reshape(-1,
3)[:,
0] = np.arange(len(sim.spin.reshape(-1, 3)[:, 0]))
# Exchange constants according to the shell
Js = np.arange(1, 10)
exch = Exchange(Js)
sim.add(exch)
field = exch.compute_field()
# We only test for the 60th lattice site
ngbs_60 = mesh.neighbours[60]
sum_ngbs = mesh._sum_ngbs_shell
# For every shell, find the ngb indexes in that shell and multiply the
# sum by the corresponding J=1, 2, 3, ...
sum_rings = 0
for i in range(1, shells + 1):
ngbs_range = slice(sum_ngbs[i - 1], sum_ngbs[i])
print('J = ', Js[i - 1], ' ngbs indexes: ', ngbs_60[ngbs_range])
sum_rings += Js[i - 1] * np.sum(ngbs_60[ngbs_range])
assert field[3 * 60] == sum_rings
def test_full_exch_hex_9_shells():
"""
Test the x component of the exchange field when using 9 shells of
neighbours in a 9 X 9 hexagonal lattice with square and diagonal
arrangement
We set J=1 for every shell and set the s_x component of the spins as the
lattice site number:
[0, 1, 2, 3, ... 80]
Since we set the s_x components as the lattice position indexes, the x
component of the field is just the sum of the indexes of the neighbours
(assuming the neighbours indexing is correct) because we set the exchange
constants as 1
"""
for arrang in ['square', 'diagonal']:
a = 1
shells = 9
mesh = HexagonalMesh(a * 0.5,
nx=9,
ny=9,
shells=shells,
alignment=arrang)
sim = Sim(mesh)
# Set s_x as the lattice site number
sim.spin.reshape(-1,
3)[:,
0] = np.arange(len(sim.spin.reshape(-1, 3)[:, 0]))
Js = np.ones(shells)
exch = Exchange(Js)
sim.add(exch)
field = exch.compute_field()
# Test the x component for every lattice site, summing the neighbours
# index and removing the -1 elements (their contribution is zero)
for i in range(sim.mesh.n):
assert field[3 * i] == np.sum(
remove_negatives(sim.mesh.neighbours[i]))
def test_exch_1d_spatial():
"""
Test the x component of the exchange field
in a 1D mesh, with the spin ordering:
0 1 2 3 4 5
"""
mesh = CuboidMesh(nx=12, ny=1, nz=1)
sim = Sim(mesh)
exch = Exchange(spatial_J)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
assert exch._J[3, 3] == -1.0
assert exch._J[5, 1] == 0.3
assert exch._J[6, 0] == 0.3
assert exch._J[8, 5] == 1.0
def test_exch_1d_spatial():
"""
Test the x component of the exchange field
in a 1D mesh, with the spin ordering:
0 1 2 3 4 5
"""
mesh = CuboidMesh(nx=12, ny=1, nz=1)
sim = Sim(mesh)
exch = Exchange(spatial_J)
sim.add(exch)
sim.set_m(init_m, normalise=False)
field = exch.compute_field()
assert exch._J[3,3] == -1.0
assert exch._J[5,1] == 0.3
assert exch._J[6,0] == 0.3
assert exch._J[8,5] == 1.0
