Nonextensive lattice gauge theories: algorithms and methods

TL;DR

This paper develops and tests generalized Monte Carlo algorithms for nonextensive lattice gauge theories based on Tsallis statistics, exploring their performance and critical behavior in high-energy physics contexts.

Contribution

It introduces a class of nonextensive heat-bath algorithms for lattice gauge simulations and analyzes their effectiveness across different Tsallis parameters.

Findings

Algorithms perform well across various q values.

Short-time dynamics reduce finite-size effects and critical slowing down.

Universality principles extend to nonextensive gauge theories.

Abstract

High-energy phenomena presenting strong dynamical correlations, long-range interactions and microscopic memory effects are well described by nonextensive versions of the canonical Boltzmann-Gibbs statistical mechanics. After a brief theoretical review, we introduce a class of generalized heat-bath algorithms that enable Monte Carlo lattice simulations of gauge fields on the nonextensive statistical ensemble of Tsallis. The algorithmic performance is evaluated as a function of the Tsallis parameter q in equilibrium and nonequilibrium setups. Then, we revisit short-time dynamic techniques, which in contrast to usual simulations in equilibrium present negligible finite-size effects and no critical slowing down. As an application, we investigate the short-time critical behaviour of the nonextensive hot Yang-Mills theory at q- values obtained from heavy-ion collision experiments. Our results imply that, when the equivalence of statistical ensembles is obeyed, the long-standing universality arguments relating gauge theories and spin systems hold also for the nonextensive framework.