Lifted Worm Algorithm for the Ising Model

TL;DR

This paper introduces an irreversible lifted worm algorithm for the Ising model, demonstrating improved dynamic behavior over reversible algorithms on different graph structures.

Contribution

The paper presents a novel lifted worm algorithm for the Ising model, enhancing dynamic efficiency compared to existing reversible methods.

Findings

Improved dynamic exponent on the complete graph

Significant constant speedup on toroidal grids

Better energy estimator performance with the lifted algorithm

Abstract

We design an irreversible worm algorithm for the zero-field ferromagnetic Ising model by using the lifting technique. We study the dynamic critical behavior of an energy estimator on both the complete graph and toroidal grids, and compare our findings with reversible algorithms such as the Prokof'ev-Svistunov worm algorithm. Our results show that the lifted worm algorithm improves the dynamic exponent of the energy estimator on the complete graph, and leads to a significant constant improvement on toroidal grids.