Global Demons in Field Theory : Critical Slowing Down in the Xy Model

TL;DR

This paper explores the use of global demons, a deterministic chaotic dynamics approach, for simulating lattice field theories, specifically analyzing critical slowing down in the 2D XY model and proposing a scheme for exact energy non-conserving algorithms.

Contribution

It introduces global demons as a novel non-local, non-Hamiltonian dynamics method for lattice field theory simulations and compares its performance to hybrid Monte Carlo in the 2D XY model.

Findings

Global demons preserve the canonical measure during simulations.

The method provides insights into critical slowing down phenomena.

A scheme for exact energy non-conserving algorithms is discussed.

Abstract

We investigate the use of global demons, a `canonical dynamics', as an approach to simulating lattice regularized field theories. This deterministically chaotic dynamics is non-local and non-Hamiltonian, and preserves the canonical measure rather than $\delta(H-E)$. We apply this inexact dynamics to the 2D XY model, comparing to various implementations of hybrid Monte Carlo, focusing on critical exponents and critical slowing down. In addition, we discuss a scheme for making energy non-conserving dynamical algorithms exact without the use of a Metropolis hit.