Microscopic Non-Universality versus Macroscopic Universality in Algorithms for Critical Dynamics

TL;DR

This paper investigates how different algorithms and lattice types influence the relaxation dynamics of spin systems near criticality, revealing universal macroscopic behavior despite early non-universal differences.

Contribution

It demonstrates that diverse algorithms and lattice configurations lead to the same universal behavior at macroscopic times, highlighting robustness in critical dynamics.

Findings

Universal behavior emerges at macroscopic times across different algorithms.

Early stages show non-universal differences depending on the method.

Universal critical dynamics are robust to algorithmic and lattice variations.

Abstract

We study relaxation processes in spin systems near criticality after a quench from a high-temperature initial state. Special attention is paid to the stage where universal behavior, with increasing order parameter emerges from an early non-universal period. We compare various algorithms, lattice types, and updating schemes and find in each case the same universal behavior at macroscopic times, despite of surprising differences during the early non-universal stages.