On the critical slowing down exponents of mode coupling theory

TL;DR

This paper introduces a static field theory-based method to compute the critical slowing down exponents in mode coupling theory, applicable to various mean-field models, and compares results with existing approaches.

Contribution

It provides a novel, dynamic-approach-independent way to determine the parameter exponent λ using static field theory and higher-order cumulants.

Findings

Method successfully applied to multiple mean-field models.

Results agree with existing dynamic approach calculations.

Offers a new perspective on critical slowing down exponents.

Abstract

A method is provided to compute the parameter exponent $\lambda$ yielding the dynamic exponents of critical slowing down in mode coupling theory. It is independent from the dynamic approach and based on the formulation of an effective static field theory. Expressions of $\lambda$ in terms of third order coefficients of the action expansion or, equivalently, in term of six point cumulants are provided. Applications are reported to a number of mean-field models: with hard and soft variables and both fully-connected and dilute interactions. Comparisons with existing results for Potts glass model, ROM, hard and soft-spin Sherrington-Kirkpatrick and p-spin models are presented.