Anomalous diffusion analysis of the lifting events in the event-chain Monte Carlo for the classical XY models

TL;DR

This paper studies a new random walk model in event-chain Monte Carlo for classical XY models, revealing superdiffusive behavior near critical points which may explain ECMC's efficiency.

Contribution

It introduces a novel random walk model in ECMC for spin systems and analyzes its anomalous diffusion properties near criticality.

Findings

The random walk in ECMC is superdiffusive near critical points.

Anomalous diffusion correlates with ECMC's performance improvement.

Numerical investigation across 1D, 2D, and 3D XY models.

Abstract

We introduce a novel random walk model that emerges in the event-chain Monte Carlo (ECMC) of spin systems. In the ECMC, the lifting variable specifying the spin to be updated changes its value to one of its interacting neighbor spins. This movement can be regarded as a random walk in a random environment with a feedback. We investigate this random walk numerically in the case of the classical XY model in 1,2, and 3 dimensions to find that it is superdiffusive near the critical point of the underlying spin system. It is suggested that the performance improvement of the ECMC is related to this anomalous behavior.