The kinetic spherical model in a magnetic field

TL;DR

This paper investigates the long-time dynamics of the spherical model under magnetic fields below critical temperature, revealing differences from Ising systems and providing exact solutions to the stochastic equations involved.

Contribution

It provides an exact reduction of the Langevin dynamics to a non-linear Volterra equation for the spherical model in a magnetic field.

Findings

Magnetization reversal dynamics resemble aging in coarsening systems.

No frequency-dependent dynamic phase transition occurs in the spherical model with oscillating fields.

Exact solution offers new insights into non-equilibrium behavior of spherical models.

Abstract

The long-time kinetics of the spherical model in an external magnetic field and below the equilibrium critical temperature is studied. The solution of the associated stochastic Langevin equation is reduced exactly to a single non-linear Volterra equation. For a sufficiently small external field, the kinetics of the magnetization-reversal transition from the metastable to the ground state is compared to the ageing behaviour of coarsening systems quenched into the low-temperature phase. For an oscillating magnetic field and below the critical temperature, we find evidence for the absence of the frequency-dependent dynamic phase transition, which was observed previously to occur in Ising-like systems.