Long-range quenched bond disorder in the bidimensional Potts model

Abstract

We study the bidimensional q-Potts model with long-range bond correlated disorder. Similarly to Chatelain (2014 Phys. Rev. E 89 032105), we implement a disorder bimodal distribution by coupling the Potts model to auxiliary spin-variables, which are correlated with a power-law decaying function. The universal behaviour of different observables, especially the thermal and the order-parameter critical exponents, are computed by Monte-Carlo techniques for q = 1 , 2 , 3 -Potts models for different values of the power-law decaying exponent a. On the basis of our conclusions, which are in agreement with previous theoretical and numerical results for q = 1 and q = 2, we can conjecture the phase diagram for q ∈ [ 1 , 4 ] . In particular, we establish that the system is driven to a fixed point at finite or infinite long-range disorder depending on the values of q and a. Finally, we discuss the role of the higher cumulants of the disorder distribution. This is done by drawing the auxiliary spin-variables from different statistical models. While the main features of the phase diagram depend only on the first and second cumulant, we argue, for the infinite disorder fixed point, that certain universal effects are affected by the higher cumulants of the disorder distribution.

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“…In the study of phase transition theory, spin models play an extremely important role, which can be divided into discrete and continuous categories. The most basic and simplest discrete model is the Ising model [8][9], which plays a crucial role in the study of phase transition theory. The slightly more complex model is the various models developed from the Ising model, such as the Potts model, the Gaussian model, the Heisenberg model, the XY model and so on.…”

Two-dimensional Ising and Potts model with long-range bond disorder: A renormalization group approach

“…We study here the two-dimensional q−Potts model with a long-range correlated bond disorder. On the basis of Monte Carlo results, we conjectured in [1] the phase diagram shown in Fig. (1).…”

“…On the basis of Monte Carlo results, we conjectured in [1] the phase diagram shown in Fig. (1). Depending on the value of the number of spin's states q and of the disorder power-law decaying exponent a, defined in Eq.…”

“…The LR point is associated to a finite strength of the disorder while the LRp is an infinite disorder one. We refer the reader to [1], and references therein, for a more general introduction to long-range disorder systems. Long-range disordered models were studied using a renormalization group (RG) approach long ago [2][3][4][5][6][7].…”

“…The long-range correlation length exponent ν SR will be computed as well at 2-loop order. [1], of the twodimensional q−Potts model with long-range bond disorder. The parameter a, on the vertical axis, is the disorder power-law decaying exponent, defined in Eq.…”