Interfacial adsorption in Potts models on the square lattice

Abstract

Abstract. We study the effect of interfacial phenomena in two-dimensional perfect and random (or disordered) q-state Potts models with continuous phase transitions, using, mainly, Monte Carlo techniques. In particular, for the total interfacial adsorption, the critical behavior, including corrections to scaling, are analyzed. The role of randomness is scrutinized. Results are discussed applying scaling arguments and invoking findings for bulk critical properties. In all studied cases, i.e., q = 3, 4, and q = 8, the spread of the interfacial adsorption profiles is observed to increase linearly with the lattice size at the bulk transition point. PACS

Interfacial adsorption in two-dimensional pure and random-bond Potts models

“…For the case of pure and randomness-induced continuous transitions we present concrete numerical evidence in favor of the standard isotropic scaling with exponents that can be traced back to the best-known estimates of the bulk critical exponent ratio β/ν of the Potts model, where β and ν are the bulk critical exponents of the order parameter and correlation length, respectively, thus reinforcing the main result of Ref. [21] for the q = 8 case. For the first-order phase transitions corresponding to the pure q = 5, 8, and q = 10 Potts models, our numerical data and scaling analysis strongly support the early scaling predictions for the size dependence of the interfacial adsorption at first-order transitions [9].…”

“…More recently, the role of randomness on the interfacial properties has been studied [21] and was found to affect, especially, the position of the interface, the excess or interfacial adsorption, and the form of the histograms resulting from the different random realizations. Still, predictions of the isotropic finite-size scaling description for the interfacial adsorption at continuous phase transitions were observed to hold, at least for the particular case of the dilute 8-states Potts model studied in Ref.…”

Ising universality in the two-dimensional Blume-Capel model with quenched random crystal field

“…Similar results have been presented in Ref. [74] for the twodimensional random-bond 8-states Potts model, where the randomness-induced continuous transition was also shown to belong to the universality class of the pure 2D Ising ferromagnet. However, the data for the case p = 0.02 are affected by strong scaling corrections [note that for the pair (L, 2L) = (24, 48), (ξ/L) * ≈ 2.5] and this is in agreement with the existence of the crossover length discussed above.…”

Monte Carlo study of the interfacial adsorption of the Blume-Capel model

“…Similar results have been presented in Ref. [9] for a few values of ∆ in the second-order transition regime but for smaller system sizes and are overall in contrast to the Potts case, where a clear diverging behavior has been observed in many relevant works [6,7,31,32]. This may be due to the different geometric nature of the interfacial adsorption among the two models, which in the present Blume-Capel model occurs in a layer-like fashion as expected on the basis of single spin-flip energy considerations, see Fig.…”

“…However, notable results in the field include the determination of critical exponents and scaling properties of the temperature and lattice-size dependencies, as well as the clarification of the fundamental role of the type of the bulk transition, with isotropic scaling holding at continuous and tricritical bulk transitions, and anisotropic scaling at bulk transitions of first-order type. More recently, a formulation of the field theory of phase separation by Delfino and colleagues has provided new insight into the problem [21][22][23][24][25][26][27][28] and, what is more, the role of randomness has been scrutinized on the basis of the disordered Potts model [29][30][31][32].…”