Investigating the nonequilibrium aspects of long-range Potts model: refinement of critical temperatures and raw exponents

TL;DR

This paper investigates the nonequilibrium critical behavior of the long-range Potts model, refining critical temperature estimates and analyzing raw exponents to understand its non-universal properties and relation to short-range systems.

Contribution

It introduces a method to determine critical temperatures and estimates raw critical exponents for the long-range Potts model, highlighting its non-universal behavior and methodological adaptability.

Findings

Critical temperature refined via optimization in short-time Monte Carlo.

Raw exponents confirm non-universality of the long-range Potts model.

Preliminary relations between long-range and short-range exponents suggested.

Abstract

In this work, we analyse the $q-$state Potts model with long-range interactions through nonequilibrium scaling relations commonly used when studying short-range systems. We determine the critical temperature via an optimization method for short-time Monte Carlo simulations. The study takes into consideration two different boundary conditions and three different values of range parameters of the couplings. We also present estimates of some critical exponents, named as raw exponents for systems with long-range interactions, which confirm the non-universal character of the model. Finally, we provide some preliminary results addressing the relations between the raw exponents and the exponents obtained for systems with short-range interactions. The results assert that the methods employed in this work are suitable to study the considered model and can easily be adapted to other systems with long-range interactions.