monte-carlo-physics

What problem does it solve?

It helps you compute physics observables and high-dimensional integrals when analytic solutions are difficult or impossible, using statistical sampling with uncertainty estimates.

Core Features & Use Cases

• Monte Carlo integration: Estimates integrals and partition-function-like quantities from random samples with error scaling ~1/sqrt(N).
• MCMC sampling: Implements Metropolis-Hastings workflows for sampling from complex target distributions and diagnosing mixing via burn-in and autocorrelation/ESS.
• Statistical mechanics simulation (Ising model): Runs Metropolis sweeps for lattice systems to study magnetization, energy, and phase-transition behavior across temperatures.
• Use Case: You need to estimate a 3D Gaussian integral and quantify the uncertainty, then simulate the 2D Ising model near the critical temperature to measure susceptibility-like response.

Quick Start

Use the monte-carlo-physics skill to run Monte Carlo integration for your target physics integral and return the estimate with a statistical error estimate.