Comment on ``Spherical 2 + p spin-glass model: An analytically solvable model with a glass-to-glass transition''

TL;DR

This paper critiques previous analyses of spherical s+p spin-glass models, suggesting that their phase behavior is not fully understood and that the 1RSB solution may be inadequate, indicating a need for further theoretical investigation.

Contribution

It highlights potential limitations of the 1RSB solution in describing the full glassy phase of spherical s+p models and calls for a reassessment of their phase behavior.

Findings

Possible glass-glass transition scenarios exist.

1RSB solution may be incorrect in the full glassy phase.

The analysis suggests the need for more accurate theoretical models.

Abstract

Guided by old results on simple mode-coupling models displaying glass-glass transitions, we demonstrate, through a crude analysis of the solution with one step of replica symmetry breaking (1RSB) derived by Crisanti and Leuzzi for the spherical $s+p$ mean-field spin glass [Phys. Rev. B 73, 014412 (2006)], that the phase behavior of these systems is not yet fully understood when $s$ and $p$ are well separated. First, there seems to be a possibility of glass-glass transition scenarios in these systems. Second, we find clear indications that the 1RSB solution cannot be correct in the full glassy phase. Therefore, while the proposed analysis is clearly naive and probably inexact, it definitely calls for a reassessment of the physics of these systems, with the promise of potentially interesting new developments in the theory of disordered and complex systems.