Thermal Brown noise¶

Physical problem¶

This page is the public physical and authoring contract for the interaction. It separates authored semantics, planner resolution, executable backend lanes, and scientific qualification.

Governing equations¶

For magnetic degree of freedom \(i\) and accepted stochastic interval \(n\),

with the implemented one-step amplitude

The bare gyromagnetic input \(\gamma_{\mu0}\) belongs in this denominator. The surrounding LLG implementation applies its Gilbert convention once; the thermal module must not apply an additional \(1/(1+\alpha^2)\) reduction.

For FDM, \(V_i=\Delta x\Delta y\Delta z\). FEM uses a documented nodal volume or mass-lumping measure. There is no standalone \(E_{\mathrm{th}}\).

Symbols and SI units¶

Stochastic integration contract¶

A fixed seed defines requested replay policy, not universal cross-device bitwise identity. Adaptive integrators must specify whether rejected trials reuse the same raw Gaussian draw and how the draw is scaled when the accepted interval changes. A deterministic ODE convergence test does not qualify an SDE implementation.

Backend capability matrix¶

Python API and stage-first example¶

# %% Study, execution lane, and magnetic body
import fullmag as fm

nm = 1.0e-9
study = fm.study("thermal_noise_reference")
study.engine("fdm")
study.device("cpu", precision="double")
study.mode("strict")
study.objects.mesh.defaults(cell_size=(2 * nm, 2 * nm, 2 * nm))
body = study.geometry(fm.Box(40 * nm, 20 * nm, 4 * nm), name="film")
body.Ms = 8.0e5
body.Aex = 13.0e-12
body.alpha = 0.02
body.m = fm.texture.uniform(1.0, 0.0, 0.0)

study.exchange()
study.thermal_noise(temperature=300.0, seed=123)
study.solver(integrator="heun", fix_dt=1.0e-15)
study.stages.add_run(stage_id="thermalize", until=1.0e-12)

Use a physical-time stage, not deterministic energy minimization. A direct H_therm output is lane-dependent; H_eff is the safer portable field observable at the audited revision.

ProblemIR¶

{"kind": "thermal_noise", "temperature": 300.0, "seed": 123}

Omitting seed requests system entropy. seed=0 is not the same state and is rejected.

Validation boundary and code hardening¶

ThermalNoise.temperature is required positive. The current Python annotation says seed: int | None, but runtime type enforcement is incomplete: positive non-integer values and booleans can pass the constructor’s seed <= 0 check. Replace this with an explicit positive-integer validator and document the exact accepted range. Planner checks remain responsible for lane, volume, timestep, material fields, and random-state availability.

Required numerical validation¶

• component mean compatible with zero;

• variance proportional to \(T\), \(\alpha\), \(1/V\), and \(1/\Delta t\);

• vanishing cross-component and cross-cell covariance;

• fixed-seed replay within one explicitly defined lane;

• rejected-step raw-draw reuse tests;

• macrospin equilibrium distribution and detailed-balance checks;

• timestep refinement under the selected stochastic interpretation;

• CPU/GPU statistical equivalence using confidence intervals, not sample equality.

Limitations and recommended extensions¶

The model does not provide longitudinal thermal fluctuations, temperature-dependent material laws, heat transport, or LLB dynamics near \(T_C\). These require separate coupled physics contracts.

Scientific bibliography¶

1. W. F. Brown, Physical Review 130, 1677–1686 (1963), DOI: 10.1103/PhysRev.130.1677.

2. J. L. García-Palacios and F. J. Lázaro, Physical Review B 58, 14937 (1998).

Control Room crosswalk¶

This is a navigation page; the selected interaction or foundation is configured by its linked Python API and object/stage editor. The category itself has no standalone control. frontend support is not implemented applies to physical parameters without a matching control. See {doc}/frontend/capability-register; do not infer UI support from backend or Python availability.

Python/API crosswalk¶

The linked Python API page is authoritative for exact functions, arguments, units, and failure semantics. If this page is a foundation or category overview, runnable Python is ot applicable here and must be taken from the terminal API page.

Bibliography and source scope¶

Use the scientific bibliography and source-code index on the linked terminal page. This block adds no new equation or unverified implementation claim.

Round-trip and failure semantics¶

Requested intent preserves the authored model, coefficients, orientations, targets, and execution request. Resolved execution records the selected solver, device, precision, discretization, and capability decision. Validation errors reject malformed or contradictory data before runtime. Unsupported combinations fail closed and are not silently omitted or converted to another interaction.

Implementation mapping¶

Python owns authoring and serialization, ProblemIR owns canonical intent, planners own legality and realization selection, and backend kernels own numerical evaluation.

Source-code index¶