Critical behaviour and ultrametricity of Ising spin-glass with long-range interactions

TL;DR

This paper investigates the critical behavior and ultrametric structure of long-range Ising spin-glass systems, revealing replica symmetry breaking features and ultrametricity in the non-mean-field regime through numerical simulations.

Contribution

It provides the first detailed numerical analysis of ultrametricity and replica symmetry breaking in long-range spin glasses outside the mean-field approximation.

Findings

Evidence of replica symmetry breaking at the critical point.

Hints of a non-trivial ultrametric structure in the configuration space.

Confirmation of critical behavior consistent with RSB in the non-mean-field regime.

Abstract

Ising spin-glass systems with long-range interactions ($J(r)\sim r^{-\sigma}$) are considered. A numerical study of the critical behaviour is presented in the non-mean-field region together with an analysis of the probability distribution of the overlaps and of the ultrametric structure of the space of the equilibrium configurations in the frozen phase. Also in presence of diverging thermodynamical fluctuations at the critical point the behaviour of the model is shown to be of the Replica Simmetry Breaking type and there are hints of a non-trivial ultrametric structure. The parallel tempering algorithm has been used to simulate the dynamical approach to equilibrium of such systems.