Estudos de modelos quânticos desordenados

Abstract

This thesis is dedicated to the investigation of magnetic phenomena in materials and their impact on their thermodynamic properties. Magnetism, in its essence, is a purely quantum phenomenon; hence, the quantum approach is indispensable for comprehending it. A brief study on the microscopic origin of magnetism, in the structure of some magnetic materials, was presented with the aim of enabling the understanding of various magnetic phenomena (ferromagnetism, paramagnetism, diamagnetism, etc.). The mean field theory approach was used in the study of three statistical lattice models (Ising, Blume-Capel, and Ising in a transverse magnetic field) with the aim of presenting the methodology used in the main works of this thesis. These models were chosen because they present different phase transitions (classical and quantum), second order, first order, in addition to the presence cca of tricritical points separating such phase transitions. The mean field theory, via Bogoliubov's inequality, was used to determine the Gibbs free energy and the equation of state (magnetization). Three cases were studied: i) the Blume-Capel model with spin S=3/2 with transverse and random single ion anisotropy, where the phase diagram and thermodynamic behavior were studies; ii) The Ising model of spin S=1 in the presence of a transverse and random magnetic field was studied and its phase diagrams and thermodynamic behavior were presented; iii) The study of the phase diagram and magnetic behavior of the Blume-Capel model, with spin S=1 with transverse and random anisotropy in a longitudinal magnetic field, was carried out.