Influence of aperiodic modulations on first-order transitions: numerical study of the two-dimensional Potts model

TL;DR

This study investigates how aperiodic modulations influence first-order phase transitions in the two-dimensional Potts model, revealing that the Harris-Luck criterion applies and that universality classes depend on the number of states and sequence type.

Contribution

It demonstrates the applicability of the Harris-Luck criterion to first-order transitions and shows the dependence of universality classes on the number of states and aperiodic sequences.

Findings

Harris-Luck criterion applies to first-order transitions.

Universality class depends on number of states and sequence.

Log-periodic behavior observed in modulated interactions.

Abstract

We study the Potts model on a rectangular lattice with aperiodic modulations in its interactions along one direction. Numerical results are obtained using the Wolff algorithm and for many lattice sizes, allowing for a finite-size scaling analyses to be carried out. Three different self-dual aperiodic sequences are employed, which leads to more precise results, since the exact critical temperature is known. We analyze two models, with six and fifteen number of states: both present first-order transitions on their uniform versions. We show that the Harris-Luck criterion, originally introduced in the study of continuous transitions, is obeyed also for first-order ones. Also, we show that the new universality class that emerges for relevant aperiodic modulations depends on the number of states of the Potts model, as obtained elsewhere for random disorder, and on the aperiodic sequence. We determine the occurrence of log-periodic behavior, as expected for models with aperiodic modulated interactions.