Dynamics of a mean spherical model with competing interactions

TL;DR

This paper analyzes the Langevin dynamics of a mean spherical model with competing interactions, revealing two distinct time scales and showing that aging effects persist despite the introduction of competing interactions.

Contribution

It provides the first detailed analysis of the dynamical behavior of a mean spherical model with competing interactions, including autocorrelation and response functions across different regimes.

Findings

Identifies two distinct time scales in the dynamics.

Derives asymptotic autocorrelation and response functions.

Shows aging effects are unaffected by competing interactions.

Abstract

The Langevin dynamics of a $d$-dimensional mean spherical model with competing interactions along $m\leq d$ directions of a hypercubic lattice is analysed. After a quench at high temperatures, the dynamical behaviour is characterized by two distinct time scales associated with stationary and aging regimes. The asymptotic expressions for the autocorrelation and response functions, in supercritical, critical, and subcritical cases, were calculated. Aging effects, which are known to be present in the ferromagnetic version of this model system, are not affected by the introduction of competing interactions.