Efficient parallel implementation of Potts model

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 ”drawback” [3,4]. The problem of these algorithms is that they are much more difficult to parallelize efficiently. Our work describes a parallel Monte Carlo solution, using a C and an MPI library, which is more efficient than the traditional methods. The Potts model consists of spins that are placed on a lattice; the lattice is usually taken to be a two-dimensional rectangular Euclidean lattice, but is often generalized to other dimensions or other lattices. The Hamiltonian function is defined as follows: H = J ∑ (i,j),(i′,j′) 1− δσ(i,j)σ(i′,j′) (1) where J is a positive constant, δ is the Kronecker delta, 1 < δ(i,j) < Nd denotes the orientation of the spin at (i, j), Nd is the number of possible domains in the system at the begining of the simulation and (i, j), (i′, j′) denotes the first neighbourhood area. The probability function is defined as: