Comportamento multicrítico no modelo de Heisenberg frustrado: transições de fases clássica e quântica

Abstract

In this work we study the critical behavior of systems described by the Anysotropic- Heisenberg model of spin 1/2 with competitive interactions (J1-J2 Model) on planes, and interplane nearest-neighbor interactions. We applied Effective-Field techniques for finite clusters with two (EFT2) and four (EFT4) central sites, as well as Linear Spin-Waves Theory (LSWT). We define &#945;=J2/J1, as the frustration parameter, which together with the the anysotropy exchange and the spatial one lambda, we obtain the respective phase diagrams. Classic phase transitions are studied at finite temperatures, as well as the quantum ones at T=0. We observed the presence of two ferromagnetic (antiferromagnetic) states, a quantum paramagnetic, colinear ferromagnetic (CF) and antiferromagnetic (CAF) at T=0 for J1 < 0 and J1 > 0. We characterized the type of transition (continuous or discontinuous) existing in them. For T > 0, the same phases are found, with the exception of the quantum and the normal paramagnetic ones. The CAF a CF states are characterized in three dimensions in the following way: spin lines with the same orientation adjacent to lines in the opposite sense, and spin planes with the same orientation adjacent to spin planes with opposite sense. In the two dimensions these two states are equivalent. We analyze the classical and quantum limits of the model through the phase destruction of PQ in the ferromagnetic and antiferromagnetic case under the influence of anisotropies. We also applied to the frustated model in the plane and the &#955; interaction between planes the Theory of Linear Spin Waves and compared their results with those found for the Effective Field Theory.