Magnetic field chaos in the SK Model

TL;DR

This paper investigates magnetic field chaos in the SK model using a modified Parallel Tempering algorithm, providing evidence for magnetic field chaos at moderate system sizes, unlike temperature chaos.

Contribution

It introduces a modified Parallel Tempering method allowing system transitions between magnetic field values and demonstrates magnetic field chaos in the SK model.

Findings

Magnetic field chaos is evident at moderate system sizes.

Temperature chaos is not observed at accessible system sizes.

The modified algorithm effectively explores the magnetic field parameter space.

Abstract

We study the Sherrington--Kirkpatrick model, both above and below the De Almeida Thouless line, by using a modified version of the Parallel Tempering algorithm in which the system is allowed to move between different values of the magnetic field h. The behavior of the probability distribution of the overlap between two replicas at different values of the magnetic field h_0 and h_1 gives clear evidence for the presence of magnetic field chaos already for moderate system sizes, in contrast to the case of temperature chaos, which is not visible on system sizes that can currently be thermalized.