A Swendsen-Wang update algorithm for the Symanzik improved sigma model

TL;DR

This paper introduces a generalized Swendsen-Wang algorithm tailored for Potts models with extended interactions, tested on a Symanzik improved sigma model, showing minimal slowing down and potential for efficient simulations.

Contribution

The paper presents a novel extension of the Swendsen-Wang algorithm for models with long-range interactions and demonstrates its effectiveness on a complex sigma model.

Findings

Minimal slowing down with a dynamic exponent z ≈ 0.3

Effective handling of long-range interactions in the model

Partial frustration affects the induced spin model dynamics

Abstract

We study a generalization of Swendsen-Wang algorithm suited for Potts models with next-next-neighborhood interactions. Using the embedding technique proposed by Wolff we test it on the Symanzik improved bidimensional non-linear $\sigma$ model. For some long range observables we find a little slowing down exponent ($z \simeq 0.3$) that we interpret as an effect of the partial frustration of the induced spin model.