Short-time dynamics in the 1D long-range Potts model

TL;DR

This paper investigates the short-time critical dynamics of the one-dimensional long-range Potts model with power-law interactions, deriving key dynamical exponents for different parameters through numerical simulations.

Contribution

It provides new numerical results on the short-time dynamics and critical exponents of the 1D long-range Potts model, extending understanding of its critical behavior.

Findings

Derived dynamical critical exponents theta' and z for q=2 and q=3.

Analyzed scaling properties of magnetization and autocorrelation functions.

Explored the effect of the interaction decay parameter sigma on critical dynamics.

Abstract

We present numerical investigations of the short-time dynamics at criticality in the 1D Potts model with power-law decaying interactions of the form 1/r^{1+sigma}. The scaling properties of the magnetization, autocorrelation function and time correlations of the magnetization are studied. The dynamical critical exponents theta' and z are derived in the cases q=2 and q=3 for several values of the parameter $\sigma$ belonging to the nontrivial critical regime.