Fields

Field realizations shared by the physics packages: Monte Carlo sampling of lattice gauge fields.

WilsonSamplingInteraction(label, *, target, beta=2.0, state='theta', move='rotate', values=(), width=1.5, rule='metropolis', schedule='colored', group=None, hits=1)

Bases: SamplingInteraction

Monte Carlo sampling of link variables with the local Wilson action of the plaquettes of a link.

For link angles the action is -beta sum_p cos(theta_p), where theta_p is the oriented sum of the link angles around the plaquette p. For the matrices of a group SU(N) it is -(beta / N) sum_p Re tr U_p, where U_p is the path-ordered product of the link matrices around p, and the move 'rotate' multiplies a link by a random matrix of the group near the identity of spread width.

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 edges of a cell complex.	required
beta	Annotated[float, ParameterSpec(domain=closed_open(0, oo))]	The inverse coupling of the Wilson action.	2.0
state	str	The name of the state that holds the link angles.	'theta'
move	str	'rotate' for U(1) or a matrix group, or 'random-value' for Z_N.	'rotate'
values	Sequence[float]	The angles a random-value move draws from.	()
width	float	The largest change of a rotation.	1.5
rule	str	The acceptance, 'metropolis', 'glauber', or 'heat-bath'.	'metropolis'
schedule	str	'colored' or 'random-sequential'.	'colored'
group	MatrixGroupSpec | None	The matrix group of the links, or None for link angles.	None
hits	int	The number of moves proposed per link and sweep of matrix links.	1

Examples:

>>> from skcomplex.systems.physics.common.fields import WilsonSamplingInteraction
>>> WilsonSamplingInteraction('wilson', target='links', beta=2.0).beta
2.0
>>> from skcomplex.core.specs import MatrixGroupSpec
>>> color = WilsonSamplingInteraction('wilson', target='links', state='U', group=MatrixGroupSpec('SU', 3))
>>> color.objective.group.degree
3

Source code in src/skcomplex/systems/physics/common/fields/_wilson_sampling.py

def __init__(
    self,
    label: str,
    *,
    target: Annotated[str, RoleSpec()],
    beta: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 2.0,
    state: str = 'theta',
    move: str = 'rotate',
    values: Sequence[float] = (),
    width: float = 1.5,
    rule: str = 'metropolis',
    schedule: str = 'colored',
    group: MatrixGroupSpec | None = None,
    hits: int = 1,
) -> None:
    super().__init__(
        label,
        target=target,
        state=state,
        objective=self._get_action if group is None else HolonomyScoreSpec(self._get_trace_action, group, hits),
        move=move,
        rule=rule,
        schedule=schedule,
        values=values,
        width=width,
    )
    self.beta = beta
    self.group = group
    self.hits = hits