We consider a nearest-neighbor p-adic Potts (with q ≥ 2 spin values and coupling constant J ∈ Qp) model on the Cayley tree of order k ≥ 1. It is proved that a phase transition occurs at k = 2, q ∈ pN and p ≥ 3 (resp. q ∈ 2N, p = 2). It is established that for p-adic Potts model at k ≥ 3 a phase transition may occur only at q ∈ pN if p ≥ 3 and q ∈ 2N if p = 2.

We apply a simple analytical criterion for locating critical temperatures to Potts models on square and triangular lattices. In the self-dual case, i. e. on the square lattice we reproduce known exact values of the critical temperature and derive the internal energy of the model at the critical point. For the Potts model on the triangular lattice we obtain very good numerical estimate of the cr...

We define a block observable for the q-state Potts model which exhibits an intermittent behaviour at the critical point. We express the intermittency indices of the normalised moments in terms of the magnetic critical exponent β/ν of the model. We confirm this relation by a numerical similation of the q = 2 (Ising) and q = 3 two-dimensional Potts model. LPTB 93-2 Mars 1993 PACS 05.70.Jk 64.60.F...

We study the q-state Potts antiferromagnet with q = 3 on the honeycomb lattice. Using an analytic argument together with a Monte Carlo simulation, we conclude that this model is disordered for all T ≥ 0. We also calculate the ground state entropy to be S0/kB = 0.507(10) and discuss this result. ∗email: [email protected] ∗∗email: [email protected] The effect of ground s...

The three-state Potts field theory in two dimensions with thermal and magnetic perturbations provides the simplest model of confinement allowing for both mesons and baryons, as well as for an extended phase with deconfined quarks. We study numerically the evolution of the mass spectrum of this model in its whole parameter range, obtaining a pattern of confinement, particle decay and phase trans...

The short-time behaviour of the critical dynamics for magnetic systems is investigated with Monte Carlo methods. Without losing the generality, we consider the relaxation process for the two dimensional Ising and Potts model starting from an initial state with very high temperature and arbitrary magnetization. We confirm the generalized scaling form and observe that the critical characteristic ...

In the solution of the superintegrable chiral Potts model special polynomials related to the representation theory of the Onsager algebra play a central role. We derive approximate analytic formulae for the zeros of particular polynomials which determine sets of low-lying energy eigenvalues of the chiral Potts quantum chain. These formulae allow the analytic calculation of the leading finite-si...

The Potts model is a powerful tool to uncover community structure in complex networks. Here, we propose a framework to reveal the optimal number of communities and stability of network structure by quantitatively analyzing the dynamics of the Potts model. Specifically we model the community structure detection Potts procedure by a Markov process, which has a clear mathematical explanation. Then...

We study the aging of the two-dimensional fully-frustrated Ising and three-state Potts models by means of Monte Carlo simulations. The system is initially prepared at infinite temperature and then quenched either at its critical temperature or in the low-temperature phase for the three-state Potts model. Autocorrelation and response functions are shown to satisfy the scaling behavior conjecture...