On the entropy of the Viana-Bray model

TL;DR

This paper analyzes the entropy of the Viana-Bray model at zero temperature, highlighting the limitations of delta function solutions and emphasizing the importance of continuous solutions for accurate modeling.

Contribution

It demonstrates that solutions considering only delta functions are unstable and fail to reproduce known results, advocating for continuous solutions in the model.

Findings

Delta function solutions are unstable and inadequate.

Continuous solutions are necessary for accurate entropy calculation.

The model aligns with Sherrington-Kirkpatrick results in the large connectivity limit.

Abstract

The entropy of the Viana-Bray model at zero temperature and external field is calculated within the solution which takes into account only delta functions for the global order parameter P(h). It is shown that such solution is unsatisfactory both from the viewpoint of stability analysis and for not reproducing the well known Sherrington-Kirkpatrick result in the large connectivity limit thus pointing out the relevance of considering solutions with continuous part in P(h) for such model and possibly related models.