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

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.

arXiv commentTo appear in Phys. Rev. E; 15 pages; 8 figures

References in corpus (10)

• Critical Behavior of Random Bond Potts Models
• Critical Behaviour of Random Bond Potts Models: A Transfer Matrix Study
• Real-Space Renormalization Group Study of the Two-dimensional Blume-Capel Model with a Random Crystal Field
• Magnetic critical behavior of two-dimensional random-bond Potts ferromagnets in confined geometries
• Blume-Emery-Griffiths Model in a Random Crystal Field
• On weak vs. strong universality in the two-dimensional random-bond Ising ferromagnet
• Aperiodicity-Induced Second-Order Phase Transition in the 8-State Potts Model
• Surface-induced disorder and aperiodic perturbations at first-order transitions
• Second-Order Phase Transition Induced by Deterministic Fluctuations in Aperiodic Eight-State Potts Models
• Non-universal behavior for aperiodic interactions within a mean-field approximation

Cited by in corpus (3)

• Griffiths phase and critical behavior of the 2D Potts models with long-range correlated disorder
• Mean-field calculation of critical parameters and log-periodic characterization of an aperiodic-modulated model
• Dynamical behavior of the Niedermayer algorithm applied to Potts models