Universal Long-Time Relaxation on the Lattices of Classical Spins: Markovian Behavior on non-Markovian Timescales

TL;DR

This paper investigates the universal long-time decay patterns of correlation functions in classical spin lattices, revealing exponential or oscillatory decay behaviors that suggest underlying chaotic dynamics despite non-Markovian timescales.

Contribution

It demonstrates the universality of long-time decay forms in classical spin systems and links this behavior to chaotic properties, challenging traditional Markovian explanations.

Findings

Long-time decay is either exponential or exponential with cosine.

Decay behavior is universal across different lattice dimensions.

Chaotic dynamics likely underpin the observed decay patterns.

Abstract

The long-time behavior of certain fast-decaying infinite temperature correlation functions on one-, two- and three-dimensional lattices of classical spins with various kinds of nearest-neighbor interactions is studied numerically, and evidence is presented that the functional form of this behavior is either simple exponential or exponential multiplied by cosine. Due to the fast characteristic timescale of the long-time decay, such a universality cannot be explained on the basis of conventional Markovian assumptions. It is suggested that this behavior is related to the chaotic properties of the spin dynamics.