Asymmetric Langevin dynamics for the ferromagnetic spherical model

TL;DR

This paper investigates how spatial asymmetry and irreversibility affect the dynamics of the ferromagnetic spherical model, revealing regimes of fluctuation-dissipation violation and providing exact analytical results across dimensions.

Contribution

It introduces an exactly solvable asymmetric Langevin dynamics for the ferromagnetic spherical model, analyzing fluctuation-dissipation violations in nonequilibrium stationary states.

Findings

Existence of weak and strong fluctuation-dissipation violation regimes.

Analytical solutions for time-dependent observables in any dimension.

Identification of a dynamical transition related to asymmetry.

Abstract

The present work pursues the investigation of the role of spatial asymmetry and irreversibility on the dynamical properties of spin systems. We consider the ferromagnetic spherical model with asymmetric linear Langevin dynamics. Such an asymmetric dynamics is irreversible, i.e., breaks detailed balance, because the principle of action and reaction is violated. The fluctuation-dissipation theorem therefore no longer holds. The stationary state is however still Gibbsian, i.e., the weights of configurations are given by the Boltzmann factor corresponding to the ferromagnetic Hamiltonian. The model is exactly solvable in any dimension, enabling an analytical evaluation of time-dependent observables. We show the existence of two regimes of violation of the fluctuation-dissipation theorem in the nonequilibrium stationary state: a regime of weak violation where the stationary fluctuation-dissipation ratio is finite but less than unity and varies continuously with the asymmetry, and a regime of strong violation where the fluctuation-dissipation ratio vanishes asymptotically. This phenomenon was first uncovered in the asymmetric kinetic Ising chain. The present results suggest that this novel kind of dynamical transition in nonequilibrium stationary states might be quite general. We also perform a systematic analysis of several regimes of interest, either stationary or transient, in various dimensions and in the different phases of the model.