Monte Carlo simulation of giant magnetoresistance

Monte Carlo method was used to simulate giant magnetoresistance in solids. A square lattice, composed by Ising spins, was generated by the usual Monte Carlo method, using periodic conditions for the borders. Resistivity was measured considering the number of clusters connected between right and left sides of the lattice, with and without applied magnetic field. The calculation of the number and surface of the connecting clusters was calculated using the Hoshen-Kopelman algorithm [1]. As we developed previously pseudorandom non-periodic numbers [2], which allows that the sizes of the clusters as big as necessary, and the steps near the transition as small as desired. This allowed a detailed study near the percolation region, over and below the magnetic transition. Three dimensional lattices, and models other than Ising for the spin coupling are natural extension of the calculation. [1]J. Hoshen and R. Kopelman, Phys. Rev. B14, 3438 (1976) [2]G.E. Barberis,Physica B 398, 468 (2007)