2014 We formulate a conjecture concerning the critical frontiers of q-state Potts ferromagnets on d-dimensional lattices (d > 1) which generalize a recent one stated for planar lattices. The present conjecture is verified within satisfactory accuracy (exactly in some cases) for all the lattices or arrays whose critical points are known. Its use leads to the prediction of : a) a considerabl...

In this paper we first show some of the bifurcation properties of Potts mean-field-theory annealing applied to traveling salesman problems. Due to these bifurcation properties, this approach, in general, produces non-optimal and non-unique solutions. As an alternative approach, we propose a nonequilibrium version of the Potts spin neural network, called chaotic Potts spin (CPS). CPS has several...

This work is a contribution to the study of universality in out-of-equilibrium lattice models undergoing a second-order phase transition at equilibrium. The experimental protocol that we have chosen is the following: the system is prepared in its high-temperature phase and then quenched at the critical temperature Tc. We investigated by mean of Monte Carlo simulations two quantities that are be...

This work is a contribution to the study of universality in out-of-equilibrium lattice models undergoing a second-order phase transition at equilibrium. The experimental protocol that we have chosen is the following: the system is prepared in its high-temperature phase and then quenched at the critical temperature Tc. We investigated by mean of Monte Carlo simulations two quantities that are be...

Cumulants of the three state Potts model and of nonequilibrium models with C 3v symmetry Abstract The critical behavior of two-dimensional stochastic lattice gas models with C 3v symmetry is analyzed. We study the cumulants of the order parameter for the three state (equilibrium) Potts model and for two irreversible models whose dynamic rules are invariant under the symmetry operations of the p...

The algebra of monodromy matrices for sl(n) trigonometric R-matrix is studied. It is shown that a generic finite-dimensional polynomial irreducible representation of this algebra is equivalent to a tensor product of L-operators. Cocommutativity of representations is discussed and inter-twiners for factorizable representations are written through the Boltzmann weights of the sl(n) chiral Potts m...

We consider the Ising model on a cylindrical lattice of L columns, with fixed-spin boundary conditions on the top and bottom rows. The spontaneous magnetization can be written in terms of partition functions on this lattice. We show how we can use the Clifford algebra of Kaufman to write these partition functions in terms of L by L determinants, and then further reduce them to m by m determinan...

We present exact calculations of the partition function for the q-state Potts model for general q, temperature and magnetic field on strips of the square lattices of width Ly = 2 and arbitrary length Lx = m with periodic longitudinal boundary conditions. A new representation of the transfer matrix for the q-state Potts model is introduced which can be used to calculate the determinant of the tr...

A brief summary of simulation techniques for recrystallization is given. The limitations of the Potts model and the Cellular Automaton model as used in their standard forms for grain growth and recrystallization are noted. A new approach based on a hybrid of the Potts model (MC) and the Cellular Automaton (CA) model is proposed in order to obtain the desired limiting behavior for both curvature...

http://dx.doi.org/10.1016/j.compgeo.2017.01.017 0266-352X/ 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). ⇑ Corresponding author at: Skempton Building, Imperial College London, SW7 2AZ, UK. E-mail addresses: [email protected] (V. Tsaparli), stavroula. [email protected] (S. Ko...