Energy fluctuations at the multicritical point in two-dimensional spin glasses

TL;DR

This study investigates energy fluctuations at the multicritical point in two-dimensional spin glasses, revealing significant sample-to-sample energy fluctuations and suggesting a geometry-induced phase transition at this critical point.

Contribution

It provides numerical evidence of energy fluctuation maxima at the multicritical point across multiple spin models, indicating a non-trivial change in bond configuration behavior.

Findings

Maximum energy fluctuations at the multicritical point

Evidence of singularity in energy fluctuations

Support for geometry-induced phase transition

Abstract

We study the two-dimensional +/-J Ising model, three-state Potts model and four-state Potts model, by the numerical transfer matrix method to investigate the behaviour of the sample-to-sample fluctuations of the internal energy on the Nishimori line. The result shows a maximum at the multicritical point in all the models we investigated. The large sample-to-sample fluctuations of the internal energy as well as the existence of a singularity in these fluctuations imply that the bond configuration (or, equivalently, the distribution of frustrated plaquettes) may be experiencing a non-trivial change of its behaviour at the multicritical point. This observation is consistent with the picture that the phase transition at the multicritical point is of geometry-induced nature.