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 6 and 15 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.

Dynamical behavior of the Niedermayer algorithm applied to Potts models

“…We then plot z versus 1/L min , as seen in Fig. 6 [17,18]. The power-law fitting for q = 3 is a good fit for all lattice sizes and we obtain z = 0.55 ± 0.02, which agrees with a previous estimate [19].…”

“…5 we present the autocorrelation time and < n > versus L for q = 3 and q = 4. To calculate z we used a different approach here [17,18]. We perform a power-law fitting using three consecutive lattice size (e.g L = 512, 1024, and 2048) and call L min the smallest size.…”

Mean-field calculation of critical parameters and log-periodic characterization of an aperiodic-modulated model

“…The interactions of the model we treat can assume one between two different values, and are ordered according to the Fibonacci aperiodic sequence. For models that have a continuous transition in its uniform version, the influence of aperiodic modulations on their critical behavior is determined by the Harris-Luck criterion [4] (which seems to hold true for models with first-order transition as well [5]). According to this criterion, the Fibonacci sequence is a marginal one; several results show that a marginal perturbation leads to a dependence of the critical exponents on the ratio between the two different interactions [6][7][8].…”