Configurational Thermometer for Lattice Gauge Theories

TL;DR

This paper introduces a gauge-invariant temperature estimator for lattice gauge theories, enabling direct thermodynamic consistency checks and diagnostics of sampling efficiency in Monte Carlo simulations.

Contribution

A novel, configuration-based temperature estimator derived from the Euclidean lattice action's gradient and Hessian, applicable across various lattice dimensions.

Findings

Successfully reproduces input temperatures in U(1) lattice gauge theories

Detects sampling inefficiencies and algorithmic artifacts

Applicable to multiple lattice dimensions

Abstract

We propose a diagnostic tool, a temperature estimator, for lattice gauge theory simulations. The estimator is obtained from the gradient and the Hessian of the Euclidean lattice action. It is gauge invariant, configuration-based, and independent of momentum-space information. These features enable direct checks of thermodynamic consistency in Monte Carlo simulations. We apply this tool to compact U(1) lattice gauge theories in one, two, and four dimensions. The results confirm the proposed estimator's ability to reproduce the input temperatures across different lattice ensembles. The estimator is sensitive to sampling inefficiencies and algorithmic artifacts, making it a useful diagnostic for large-scale simulations.