Compressible Sherrington-Kirkpatrick spin-glass model

TL;DR

This paper introduces a spin-glass model with elastic degrees of freedom, analyzing its phase diagram and phase transitions using the replica method, and relating findings to hydrogen-bonded crystal mixtures.

Contribution

It presents a novel spin-glass model incorporating elasticity and provides a detailed phase diagram analysis using replica symmetry.

Findings

Identified critical boundaries between disordered and ordered phases.

Discovered a tricritical point where the transition changes from second to first order.

Connected theoretical results to experimental phase diagrams of hydrogen-bonded crystals.

Abstract

We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica method. In the replica-symmetric approximation, we analyze the pressure-temperature phase diagram, and obtain expressions for the critical boundaries between the disordered and the ordered (spin-glass and ferromagnetic) phases. The second-order para-ferromagnetic border ends at a tricritical point, beyond which the transition becomes discontinuous. We use these results to make contact with the temperature-concentration phase diagrams of mixtures of hydrogen-bonded crystals.