An autoassociative network of Potts units, coupled via tensor connections, has been proposed and analysed as an effective model of an extensive cortical network with distinct shortand long-range synaptic connections, but it has not been clarified in what sense it can be regarded as an effective model. We draw here the correspondence between the two, which indicates the need to introduce a local...

A new graphical method is developed to calculate the critical temperature of 2and 3-dimensional Ising models as well as that of the 2-dimensional Potts models. This method is based on the transfer matrix method and using the limited lattice for the calculation. The reduced internal energy per site has been accurately calculated for different 2-D Ising and Potts models using different size-limit...

-In this work, we use Potts neurons for the competitive mechanism in a self-organization model. We obtain new algorithms on the basis of a Potts neural network for coherent mapping, and we remodel the Durbin algorithm and the Kohonen algorithm with mean field annealing. The resulting dimension-reducing mappings possess a highly reliable topology preservation such that the nearby elements in the...

for their sedulous help and encouragement. Many thanks to my friends and my mother.

The universal amplitude ratio R̃ ξ for percolation in two dimensions is determined exactly using results for the dilute A model in regime 1, by way of a relationship with the q-state Potts model, with q 6 4. The numerical result obtained by Delfino and Cardy by quantum field theory techniques agrees well with the algebraic expression determined here. Percolation is a subject which can be describ...

In this work we present a different approach to simulate the Ferromagnetic Potts model [1] described by Renfrey B. Potts in 1952 and it is a generalization of the Ising [2] model. It is well-known that the Potts model has a disadvantage when it is implemented using a Monte Carlo simulation with a standard Metropolis algorithm. Many parallel algorithms have recently been developed to reduce this...

The Yang-Lee zeros of the Q-state Potts model on recursive lattices are studied for noninteger values of Q. Considering one-dimensional (1D) lattice as a Bethe lattice with coordination number equal to 2, the location of Yang-Lee zeros of 1D ferromagnetic and antiferromagnetic Potts models is completely analyzed in terms of neutral periodical points. Three different regimes for Yang-Lee zeros a...

We consider the ferromagnetic q-state Potts model, with each of the q spin values coupled to an external field. We also introduce a generalized random cluster model, which includes both the Potts model in arbitrary homogeneous external fields and the non-integer q random cluster model as special cases. We establish the FKG property, the finite energy condition, uniqueness of the infinite cluste...