Ensemble Inequivalence in the Ferromagnetic p-spin Model in Random Fields

TL;DR

This paper investigates how randomness affects long-range ferromagnetic p-spin models, revealing ensemble inequivalence, negative specific heat, and ergodicity breaking, especially for p>2, challenging traditional thermodynamic descriptions.

Contribution

It demonstrates the fundamental differences in phase diagrams between canonical and microcanonical ensembles for p>2 in disordered long-range systems.

Findings

For p=2, phase diagram resembles known models with ensemble inequivalence features.

For p>2, canonical and microcanonical phase diagrams differ significantly.

Negative specific heat appears in ferromagnetic phases at low external fields for p>2.

Abstract

We study the effect that randomness has on long-range interacting systems by using the ferromagnetic Ising model with $p$-body interactions in random fields. The case with p=2 yields a phase diagram similar to that of previously studied models and shows known features that inequivalence of the canonical and microcanonical ensembles brings with it, for example negative specific heat in a narrow region of the phase diagram. When p>2, however, the canonical phase diagram is completely different from the microcanonical one. The temperature does not necessarily determine the microcanonical phases uniquely, and thus the ferromagnetic and paramagnetic phases are not separated in such a region of a conventional phase diagram drawn with the temperature and field strength as the axes. Below a certain value of the external field strength, part of the ferromagnetic phase has negative specific heat. For large values of the external field strength the ergodicity is broken before the phase transition occurs for p>2. Moreover, for p>2, the Maxwell construction cannot be derived in a consistent manner and therefore, in contrast to previous cases with negative specific heat, the Maxwell construction does not bridge the gap between the ensembles.