Second-order phase transition induced by deterministic fluctuations in aperiodic eight-state Potts models

Abstract

We investigate the influence of aperiodic modulations of the exchange interactions between nearest-neighbour rows on the phase transition of the two-dimensional eight-state Potts model. The systems are studied numerically through intensive Monte Carlo simulations using the Swendsen-Wang cluster algorithm for different aperiodic sequences. The transition point is located through duality relations, and the critical behaviour is investigated using FSS techniques at criticality. While the pure system exhibits a first-order transition, we show that the deterministic fluctuations resulting from the aperiodic coupling distribution are liable to modify drastically the physical properties in the neighbourhood of the transition point. For strong enough fluctuations of the sequence under consideration, a second-order phase transition is induced. The exponents β/ν, γ/ν and (1 − α)/ν are obtained at the new fixed point and crossover effects are discussed. Surface properties are also studied.

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

“…The models we treat are invariant under a duality transformation, and the exact critical temperature (k B T c /J A ) is known [16,17]. This knowledge allows for a more precise calculation of critical exponents, using finite-size scaling, but the simulation at T c also leads to a severe critical-slowing down if a single-spin algorithm, such as Metropolis [22], for example, is used.…”

“…When > 0 the sequence is relevant, and when < 0 the sequence is irrelevant. This criterion applies to continuous transitions in the uniform model, but numerical results [16,17] indicate that it holds true also when the transition in the original model is a first-order one (if this is the case, the introduction of aperiodic modulations on the interaction parameters leads to a scenario totally different from the one for random disorder). This result was established through a study of the ferromagnetic Potts model [18] with q = 8 states in Refs.…”

“…This result was established through a study of the ferromagnetic Potts model [18] with q = 8 states in Refs. [16] and [17]; in this model a dynamical variable with q states is assigned to each site on a given lattice, and first-neighbor sites tend to be in the same state (see below). For low enough q, the transition is continuous, while it is first order for q above a given value q c (in two-dimensional lattices, q c = 4).…”

Quasiperiodic fluctuation effect on a first-order phase transition: A Monte Carlo investigation

“…The ratio JЈ/J has been fixed according to previous studies 12, 13 which have indicated that 10 is a convenient value. Note that, unlike most of the other studies, [11][12][13]19,37 the transition temperature of the infinite system is unknown. The order parameter m has been defined by 37…”

“…The divergence of these fluctuations is characterized by the wandering exponent . 18,19 Their effect on a second-order phase transition can be predicted from Luck's criterion. 18 Concerning a first-order transition, a nonrigorous generalization of this criterion consists in replacing the correlation length exponent by 1/d ͑d is the dimensionality of the lattice͒.…”