First-order transition in the one-dimensional three-state Potts model with long-range interactions

TL;DR

This paper investigates how the nature of phase transitions in a one-dimensional three-state Potts model with long-range interactions changes with the decay parameter, using numerical simulations and scaling analysis.

Contribution

It introduces a detailed numerical study of the transition from second-order to first-order phase transitions as the interaction decay parameter varies.

Findings

Identifies the critical value of the decay parameter where the transition changes character.

Demonstrates the effectiveness of the Luijten-Bl"ote algorithm for simulating long-range interactions.

Provides scaling analysis linking interface free energy, Binder's cumulant, and specific heat to transition type.

Abstract

The first-order phase transition in the three-state Potts model with long-range interactions decaying as $1/r^{1+\sigma}$ has been examined by numerical simulations using recently proposed Luijten-Bl\"ote algorithm. By applying scaling arguments to the interface free energy, the Binder's fourth-order cumulant, and the specific heat maximum, the change in the character of the transition through variation of parameter $\sigma$ was studied.