Discrete Laplacian Thermostat for Spin Systems with Conserved Dynamics

TL;DR

This paper introduces a stochastic conservative thermostat for spin systems that efficiently relaxes magnetic energy while preserving conserved quantities, accurately reproducing critical behavior and spin wave phenomena without simulating the lattice.

Contribution

The paper presents a novel discrete Laplacian thermostat that conserves constants of motion and models realistic energy relaxation in spin systems without explicit lattice simulation.

Findings

Reproduces exact static and dynamic critical exponents in 3D Heisenberg antiferromagnet

Yields correct spin wave phenomenology in low-temperature phase

Quantitatively links relaxation coefficient to microscopic spin-lattice coupling parameters

Abstract

A well-established numerical technique to study the dynamics of spin systems in which symmetries and conservation laws play an important role is to microcanonically integrate their reversible equations of motion, obtaining thermalization through initial conditions drawn with the canonical distribution. In order to achieve a more realistic relaxation of the magnetic energy, numerically expensive methods that explicitly couple the spins to the underlying lattice are normally employed. Here we introduce a stochastic conservative thermostat that relaxes the magnetic energy while preserving the constant of motions, thus turning microcanonical spin dynamics into a conservative canonical dynamics, without actually simulating the lattice. We test the thermostat on the Heisenberg antiferromagnet in d=3 and show that the method reproduces the exact values of the static and dynamic critical exponents, while in the low-temperature phase it yields the correct spin wave phenomenology. Finally, we demonstrate that the relaxation coefficient of the new thermostat is quantitatively connected to the microscopic parameters of the spin-lattice coupling.