Nonflat Histogram Techniques for Spin Glasses

TL;DR

This paper introduces a modified ensemble technique using power-law-shaped histograms for spin glasses, which significantly speeds up sampling compared to traditional flat-histogram methods.

Contribution

It proposes a novel energy histogram modification that enhances sampling efficiency in spin glass simulations beyond existing methods.

Findings

Power-law histograms reduce mean round-trip times.

The method outperforms standard multicanonical sampling.

Speed-up observed across multiple lattice sizes.

Abstract

We study the bimodal Edwards-Anderson spin glass comparing established methods, namely the multicanonical method, the $1/k$-ensemble and parallel tempering, to an approach where the ensemble is modified by simulating power-law-shaped histograms in energy instead of flat histograms as in the standard multicanonical case. We show that by this modification a significant speed-up in terms of mean round-trip times can be achieved for all lattice sizes taken into consideration.