Spins

Spin realizations shared by the physics packages: Ising spins and the Monte Carlo sampling of Ising spins.

IsingSamplingInteraction(label, *, target, state='spin', rule='metropolis', schedule='checkerboard', neighborhood=None)

Bases: SpinSamplingInteraction

Monte Carlo sweeps of Ising spins s = ±1 of local energy -J s sum_j s_j - h s, by flips.

The coupling J, the field h, and the temperature are parameters of the spins.

Parameters:

Name	Type	Description	Default
label	str	The label of the interaction, unique among the parts of its system.	required
target	Annotated[str, RoleSpec()]	The path of the group of spins.	required
state	str	The name of the state that holds the spin.	'spin'
rule	str	The acceptance, 'metropolis', 'glauber', or 'heat-bath'.	'metropolis'
schedule	str	'checkerboard' on a square lattice, 'colored' on a network, or 'random-sequential'.	'checkerboard'
neighborhood	BaseNeighborhood | None	The neighbours of a spin, or None for the von Neumann neighbourhood. A network takes AdjacencyNeighborhood().	None

Examples:

>>> from types import SimpleNamespace
>>> from sage.all__sagemath_symbolics import var
>>> from skcomplex.systems.physics.common.spins import IsingSamplingInteraction
>>> ising = IsingSamplingInteraction('ising', target='spins')
>>> other = SimpleNamespace(spin=var('t'))
>>> ising.energy(SimpleNamespace(target=SimpleNamespace(spin=var('s'), J=1, h=var('h'), other=other)))
-h*s - s*neighbors(t, reduce='sum')

Source code in src/skcomplex/systems/physics/common/spins/_ising_sampling.py

def __init__(
    self,
    label: str,
    *,
    target: Annotated[str, RoleSpec()],
    state: str = 'spin',
    rule: str = 'metropolis',
    schedule: str = 'checkerboard',
    neighborhood: BaseNeighborhood | None = None,
) -> None:
    super().__init__(
        label,
        target=target,
        state=state,
        energy=self._energy,
        rule=rule,
        schedule=schedule,
        neighborhood=neighborhood,
    )

IsingSpinElement(label, visual=None, *, spin=1.0, J=1.0, h=0.0, temperature=2.0)

Bases: Element

Ising spin, up at 1 or down at -1, with its coupling J, its field h, and its temperature.

An IsingSamplingInteraction flips the spins by Monte Carlo sweeps at the temperature of the spins.

Parameters:

Name	Type	Description	Default
label	str	The label of the spin or the lattice group.	required
visual	VisualSpec | None	How the spin is drawn, or None for default_visual_.	None
spin	Annotated[float, StateSpec(domain=ZZ)]	The initial spin, 1 or -1.	1.0
J	Annotated[float, ParameterSpec()]	The coupling between neighbouring spins.	1.0
h	Annotated[float, ParameterSpec()]	The external field.	0.0
temperature	Annotated[float, ParameterSpec(domain=open(0, oo))]	The temperature in units of the coupling.	2.0

Attributes:

Name	Type	Description
default_visual_		The visual of the spin when it sets none.

Examples:

>>> from skcomplex.systems.physics.common.spins import IsingSpinElement
>>> IsingSpinElement('spin').temperature
2.0

Source code in src/skcomplex/systems/physics/common/spins/_ising_spin.py

def __init__(
    self,
    label: str,
    visual: VisualSpec | None = None,
    *,
    spin: Annotated[float, StateSpec(domain=ZZ)] = 1.0,
    J: Annotated[float, ParameterSpec()] = 1.0,
    h: Annotated[float, ParameterSpec()] = 0.0,
    temperature: Annotated[float, ParameterSpec(domain=RealSet.open(0, oo))] = 2.0,
) -> None:
    super().__init__(label, visual=visual)
    self.spin = spin
    self.J = J
    self.h = h
    self.temperature = temperature

SpinSamplingInteraction(label, *, target, state, energy, move='flip', rule='metropolis', schedule='checkerboard', neighborhood=None, values=(), width=1.0)

Bases: ThermalSamplingInteraction

Monte Carlo sweeps of the spins of a lattice or network group at the temperature of the spins.

The temperature is the parameter temperature of the spins, so it lives with the couplings and fields of the spins, and a schedule of <group>.temperature changes it during a run. The local energy reads the states and parameters of the spin as namespace.target.

Parameters:

Name	Type	Description	Default
label	str	The label of the interaction, unique among the parts of its system.	required
target	Annotated[str, RoleSpec()]	The path of the group of spins.	required
state	str	The name of the state the moves change.	required
energy	Callable[[SimpleNamespace], object]	The function energy(namespace) of the local energy of a spin.	required
move	str | Callable[..., object]	'flip', 'random-value', 'rotate', 'gaussian', or a function that proposes values.	'flip'
rule	str	The acceptance, 'metropolis', 'glauber', or 'heat-bath'.	'metropolis'
schedule	str	'checkerboard', 'colored', or 'random-sequential'.	'checkerboard'
neighborhood	BaseNeighborhood | None	The neighbourhood the energy reduces over, or None for the von Neumann neighbourhood.	None
values	Sequence[float]	The values a random-value move draws from.	()
width	float	The largest change of a rotation, or the standard deviation of a Gaussian move.	1.0

Examples:

>>> from skcomplex.core.components.laws.utils import neighbors
>>> from skcomplex.systems.physics.common.spins import SpinSamplingInteraction
>>> energy = lambda n: -n.target.spin * neighbors(n.target.other.spin)
>>> SpinSamplingInteraction('ising', target='spins', state='spin', energy=energy).rule
'metropolis'

Source code in src/skcomplex/systems/physics/common/spins/_spin_sampling.py

def __init__(
    self,
    label: str,
    *,
    target: Annotated[str, RoleSpec()],
    state: str,
    energy: Callable[[SimpleNamespace], object],
    move: str | Callable[..., object] = 'flip',
    rule: str = 'metropolis',
    schedule: str = 'checkerboard',
    neighborhood: BaseNeighborhood | None = None,
    values: Sequence[float] = (),
    width: float = 1.0,
) -> None:
    super().__init__(
        label,
        target=target,
        state=state,
        energy=energy,
        move=move,
        rule=rule,
        schedule=schedule,
        neighborhood=neighborhood,
        values=values,
        width=width,
    )

ThermalSamplingInteraction(label, *, target, state, energy, move='flip', temperature=1.0, rule='metropolis', schedule='checkerboard', neighborhood=None, values=(), width=1.0, cooling=None)

Bases: SamplingInteraction

Monte Carlo sweeps of a state in an energy at a temperature, the intensity one over the temperature.

Parameters:

Name	Type	Description	Default
label	str	The label of the interaction, unique among the parts of its system.	required
target	Annotated[str, RoleSpec()]	The path of the group on the sites of a lattice or the nodes of a network.	required
state	str	The name of the state the moves change.	required
energy	Callable[[SimpleNamespace], object]	The function energy(namespace) of the local energy of a member.	required
move	str | Callable[..., object]	'flip', 'random-value', 'rotate', 'gaussian', 'cluster', or a function that proposes values.	'flip'
temperature	Annotated[float, ParameterSpec(domain=closed_open(0, oo))]	The temperature, where 0 accepts only moves that do not raise the energy.	1.0
rule	str	The acceptance, 'metropolis', 'glauber', or 'heat-bath', which draws among all values of a discrete move by their Boltzmann weights.	'metropolis'
schedule	str	'checkerboard', 'colored', or 'random-sequential'.	'checkerboard'
neighborhood	BaseNeighborhood | None	The neighbourhood the energy reduces over, or None for the von Neumann neighbourhood.	None
values	Sequence[float]	The values a random-value move draws from.	()
width	float	The largest change of a rotation, or the standard deviation of a Gaussian move.	1.0
cooling	Callable[[Expression], object] | None	The function of the time symbol that multiplies the temperature, or None for a constant temperature.	None

Examples:

>>> from skcomplex.core.components.laws.utils import neighbors
>>> from skcomplex.systems.physics.common.spins import ThermalSamplingInteraction
>>> energy = lambda n: -n.target.s * neighbors(n.target.other.s)
>>> ThermalSamplingInteraction('ising', target='spins', state='s', energy=energy, temperature=2.0).temperature
2.0

Source code in src/skcomplex/systems/physics/common/spins/_thermal_sampling.py

def __init__(
    self,
    label: str,
    *,
    target: Annotated[str, RoleSpec()],
    state: str,
    energy: Callable[[SimpleNamespace], object],
    move: str | Callable[..., object] = 'flip',
    temperature: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 1.0,
    rule: str = 'metropolis',
    schedule: str = 'checkerboard',
    neighborhood: BaseNeighborhood | None = None,
    values: Sequence[float] = (),
    width: float = 1.0,
    cooling: Callable[[Expression], object] | None = None,
) -> None:
    super().__init__(
        label,
        target=target,
        state=state,
        objective=energy,
        move=move,
        rule=rule,
        schedule=schedule,
        neighborhood=neighborhood,
        values=values,
        width=width,
        cooling=cooling,
    )
    self.energy = energy
    self.temperature = temperature