Cluster Monte Carlo algorithms for diluted spin glasses

TL;DR

This paper extends cluster Monte Carlo algorithms to three-dimensional diluted spin glass models, demonstrating their efficiency and providing evidence for a spin glass transition at a specific site occupation.

Contribution

It introduces and compares cluster Monte Carlo algorithms for 3D diluted spin glasses, showing their effectiveness and identifying a transition point.

Findings

Algorithms are effective in 3D diluted EA models.

Evidence of a spin glass transition at p=62.5%.

Comparison with parallel tempering shows competitive efficiency.

Abstract

Recently a cluster Monte Carlo algorithm has been used very successfully in the two-dimensional Edwards-Anderson (EA) model. We show that this algorithm and a variant thereof can also be used successfully in models with a non-zero spin glass transition temperature. The application of such algorithms to the site-diluted EA model in three dimensions is discussed and the efficiency of the two algorithms is compared among each other and to parallel tempering. Finally, we give evidence for a spin glass transition in the three-dimensional site-diluted EA model with Gaussian couplings at a site occupation of p = 62.5 %.