Análise de frustração em sistemas antiferromagnéticos

Abstract

In this work, we study the thermodynamics of ferromagnetic and antiferromagnetic materials described by the Hamiltonian of the two-dimensional isotropic spin Heisenberg model. We consider the Ising model with two spin lattices (i.e. triangular and square), assuming first neigh- bors interactions only. We solve both lattices analytically and numerically. For the analytical solution, we find the thermodynamic properties of the system identifying the partition function. For the numerical solutions, we apply the mean field theory with the Metropolis and Monte Carlo methods. We have observed that, for different topologies, ferromagnetic materials show the same behaviour of their thermodynamic properties in both lattices. Whereas antiferromag- netic materials are quite different, due to the frustration phenomenon. This phenomenon is characteristic of antiferromagnetic materials. It occurs when the spin can not be oriented to minimize the interaction energy with all neighbors. In general, this occurs when the lattice site connectivity is odd (e.g. triangular). The thermodynamic properties extracted for those lattices were: total system energy, specific heat, magnetization and magnetic susceptibility.