Monte Carlo em redes de Spins aplicado a estruturas percolantes

Abstract

This work is to study two-dimensional and three-dimensional magnetic systems percolating out of balance with an order parameter maintained - our order parameter is the total magnetization. These studies are restricted to the processes that occur at intervals of time (time mean the number of steps in the simulation process) near the start of the simulation. The behavior of sitemas at the beginning of the temporal evolution features or not systems as having slow relaxation. Our understanding of what slow relaxation and percolation are described in the text of the thesis. The simulations that we will be making take into account stochastic processes namely processes like Monte Carlo. Through the total energy of the system’s behavior mapping and / or other structural property as clusters of borders, we check whether the studied systems have fractal behavior or not. We shall see that there is an intimate relationship between the fractal behavior and the nature of the distribution of spins in the system. The magnetic systems mentioned above are generated with a certain probability distribution of the spins in the network, associated with the respective probabilities of percolation (pc) already determined in the literature that is, in the case of square two-dimensional networks have pc = 0.5927 and the simple cubical pc = 0.3116. We will see that both systems (two- or three-dimensional) have fractal behavior and slow relaxation, with the two-dimensional case presenting situations that can not be characterized thereby presenting three-dimensional relaxation while only slow relaxation. I would like to place on record ready, this work is novel because there is no report in the literature to date, the three-dimensional systems to study the way we make. Added up to this fact, the innovative description of a methodological approach to a problem that does not possess phase transition at finite temperature.