On generalized cluster algorithms for frustrated spin models

TL;DR

This paper explores a generalized cluster algorithm for frustrated spin models, demonstrating its effectiveness for simple models and limitations for complex systems like spin glasses.

Contribution

It introduces a practical methodology for constructing generalized cluster algorithms and evaluates their performance on various frustrated spin models.

Findings

Works well for simple 2D fully frustrated Ising models

Performs poorly or not at all for complex models like spin glasses

Provides insights into algorithm design for frustrated systems

Abstract

Standard Monte Carlo cluster algorithms have proven to be very effective for many different spin models, however they fail for frustrated spin systems. Recently a generalized cluster algorithm was introduced that works extremely well for the fully frustrated Ising model on a square lattice, by placing bonds between sites based on information from plaquettes rather than links of the lattice. Here we study some properties of this algorithm and some variants of it. We introduce a practical methodology for constructing a generalized cluster algorithm for a given spin model, and investigate apply this method to some other frustrated Ising models. We find that such algorithms work well for simple fully frustrated Ising models in two dimensions, but appear to work poorly or not at all for more complex models such as spin glasses.