Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions

TL;DR

This paper uses Monte Carlo simulations to study the one-dimensional Ising spin glass with power-law interactions, providing evidence for replica symmetry breaking and analyzing domain wall energies at low temperatures.

Contribution

It introduces large-scale droplet excitation analysis and zero-temperature defect energy calculations for the model, comparing results with analytic predictions.

Findings

Evidence for large-scale droplet excitations with size-independent energy.

Observation of replica symmetry breaking behavior.

Measured stiffness exponents with partial agreement to theory.

Abstract

We present results from Monte Carlo simulations of the one-dimensional Ising spin glass with power-law interactions at low temperature, using the parallel tempering Monte Carlo method. For a set of parameters where the long-range part of the interaction is relevant, we find evidence for large-scale droplet-like excitations with an energy that is independent of system size, consistent with replica symmetry breaking. We also perform zero-temperature defect energy calculations for a range of parameters and find a stiffness exponent for domain walls in reasonable, but by no means perfect agreement with analytic predictions.