Bond diluted Levy spin-glass model and a new finite size scaling method to determine a phase transition

TL;DR

This paper investigates spin-glass phase transitions in a diluted long-range Ising model, introducing a new finite size scaling method that can be applied even below the upper critical dimension and in magnetic fields.

Contribution

It presents a novel finite size scaling approach for detecting spin-glass transitions in diluted long-range models, applicable in magnetic fields and below the upper critical dimension.

Findings

Evidence of spin-glass transition in systems below the upper critical dimension

Validation of a new finite size scaling method

Applicability of the method in magnetic fields

Abstract

A spin-glass transition occurs both in and out of the limit of validity of mean-field theory on a diluted one dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance. Varying the power in this long-range model corresponds, in a one-to-one relationship, to change the dimension in spin-glass short-range models. Using different finite size scaling methods evidence for a spin-glass transition is found also for systems whose equivalent dimension is below the upper critical dimension at zero magnetic field. The application of a new method is discussed, that can be exported to systems in a magnetic field.