Neste trabalho apresentamos uma discussão detalhada sobre as curvas de histerese obtidas no caso do mais simples sistema magnético, o modelo de Ising. As curvas de histerese são construídas através de estados estáveis e metaestáveis do sistema. A estabilidade de cada estado é determinada pela energia livre de Gibbs do sistema para cada valor de temperatura e campo magnético externo. Também discutimos o procedimento necessário para a determinação de curvas de histerese através do método de Monte Carlo, de forma a manter o sistema em seus estados metaestáveis durante as simulações.

In this work we present a detailed discussion concerning the hysteresis curves for the simplest magnetic system, the Ising model. The hysteresis curves are generated by passing along a set of stable and metastable states of the system. The stability of each state is determined by the Gibbs free energy of the system for each pair of values of temperature and field. We also discuss how we must proceed in determining hysteresis curves by the Monte Carlo method in order to keep the system in its metastable states during the simulation process.

We investigate the equilibrium magnetic properties of a simple cubic small ferromagnetic particle under an external magnetic field. Although the particle is small, it can not be considered as a single-domain unit. The magnetic moments are represented by unitary spin vectors and we consider ferromagnetic interactions between nearest-neighbor spins. The coupling between spins is given in terms of the classical Heisenberg Hamiltonian and we also include a Zeeman contribution and a single-ion uniaxial anisotropy. The size of the particle changes from one to twelve lattice spacings. We employ in our study mean-filed calculations and Monte Carlo simulations. The magnetization and susceptibility curves as a function of temperature show that an uniaxial anisotropy can mimic a ferromagnetic or an antiferromagnetic coupling, depending on the angle between the external magnetic field and the easy axis.