The Complexity of the Spherical $p$-spin spin glass model, revisited

TL;DR

This paper reviews and refines the methods for calculating the complexity and number of metastable states in the spherical p-spin spin glass model, providing a detailed step-by-step analysis.

Contribution

It offers a comprehensive review and clarification of the calculation procedures for complexity in the spherical p-spin model, highlighting methodological improvements.

Findings

Clarified the calculation steps for complexity

Identified key assumptions in the model

Enhanced understanding of metastable state enumeration

Abstract

Some questions concerning the calculation of the number of ``physical'' (metastable) states or complexity of the spherical $p$-spin spin glass model are reviewed and examined further. Particular attention is focused on the general calculation procedure which is discussed step-by-step.