Inverse freezing in the Hopfield Fermionic Ising Spin Glass

TL;DR

This paper investigates how frustration influences inverse freezing in the Hopfield fermionic spin glass model, revealing that reducing frustration suppresses the reentrant phase transition associated with inverse freezing.

Contribution

It introduces a detailed analysis of the role of frustration in inverse freezing within the Hopfield fermionic spin glass model, using path integral formalism and replica symmetry breaking.

Findings

Inverse freezing is suppressed as frustration decreases.

Phase diagrams show reentrance diminishes with less frustration.

Frustration level critically affects the occurrence of inverse freezing.

Abstract

In this work it is studied the Hopfield fermionic spin glass model which allows interpolating from trivial randomness to a highly frustrated regime. Therefore, it is possible to investigate whether or not frustration is an essential ingredient which would allow this magnetic disordered model to present naturally inverse freezing by comparing the two limits, trivial randomness and highly frustrated regime and how different levels of frustration could affect such unconventional phase transition. The problem is expressed in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann variables. The Grand Canonical Potential is obtained within the static approximation and one-step replica symmetry breaking scheme. As a result, phase diagrams temperature {\it versus} the chemical potential are obtained for several levels of frustration. Particularly, when the level of frustration is diminished, the reentrance related to the inverse freezing is gradually suppressed.