Ferromagnetic to paramagnetic transition in spherical spin glass

TL;DR

This paper investigates the phase transition between ferromagnetic and paramagnetic states in a spherical spin glass model combining Sherrington-Kirkpatrick and Curie-Weiss Hamiltonians, analyzing fluctuations at the critical scale.

Contribution

It characterizes the critical transition between ferromagnetic and paramagnetic phases in a combined spherical spin glass model, including fluctuation analysis.

Findings

Identifies the phase boundary between ferromagnetic and paramagnetic regimes.

Analyzes free energy fluctuations at the critical transition.

Provides a detailed phase diagram with three regimes.

Abstract

We consider the spherical spin glass model defined by a combination of the pure 2-spin spherical Sherrington-Kirkpatrick Hamiltonian and the ferromagnetic Curie-Weiss Hamiltonian. In the large system limit, there is a two-dimensional phase diagram with respect to the temperature and the coupling strength. The phase diagram is divided into three regimes; ferromagnetic, paramagnetic, and spin glass regimes. The fluctuations of the free energy are known in each regime. In this paper, we study the transition between the ferromagnetic regime and the paramagnetic regime in a critical scale.