Nature of the Spin Glass Phase in Finite Dimensional (Ising) Spin Glasses

TL;DR

This paper investigates the fundamental nature of the spin glass phase in finite-dimensional systems through analytical and numerical methods, addressing critical properties, phase transitions, and theoretical debates.

Contribution

It provides new analytical and numerical insights into the critical behavior, phase transition existence, and rigorous results for finite-dimensional spin glasses, comparing different theoretical frameworks.

Findings

Critical exponents at the phase transition identified

Existence of a phase transition in a magnetic field demonstrated

Numerical construction of the Aizenman-Wehr metastate performed

Abstract

Spin glasses are the paradigm of complex systems. These materials present really slow dynamics. However, the nature of the spin glass phase in finite dimensional systems is still controversial. Different theories describing the low temperature phase have been proposed: droplet, replica symmetry breaking and chaotic pairs. We present analytical studies of critical properties of spin glasses, in particular, critical exponents at and below the phase transition, existence of a phase transition in a magnetic field, computation of the lower critical dimension (in presence/absence of a magnetic field). We also introduce some rigorous results based on the concept of metastate. Finally, we report some numerical results regarding the construction of the Aizenman-Wehr metastate, scaling of the correlation functions in the spin glass phase and existence of a phase transition in a field, confronting these results with the predictions of different theories.