Modelo Vidro de Spin Fermiônico com Campos Transverso e Longitudinal Aleatórios

Abstract

The present work studies the behaviors of linear and non-linear magnetic sus ceptibilities, as parameters of order of spin glass q and of the Almeida-Thouless line λAT , using the Fermionic Ising Spin Glass Model (FISG) with both random transverse and longitudinal fields. The motivation of this work is in the controversy about the existence, or not, of a phase transition of spin glass (SG) in the compound LiHoxY1−xF4. This com pound, in the low dilution regime x = 0.167, presents a peculiar behavior in the non-linear magnetic susceptibility χ3, which has been a source of controversy in its interpretation. In the absence of an applied transverse field Bx, χ3 presents a divergence in a tempera ture Tf , which indicates a second order SG phase transition. However, in the presence of Bx, the divergence in χ3 is replaced by a rounded maximum, located at a temperature T ∗ . In this case T ∗ < Tf , which means that the maximum temperature T ∗ is lower than the phase transition temperature Tf when Bx is absent. It is suggested that this beha vior occurs due to the presence of random fields, which are induced through the applied transverse field. Another important behavior observed experimentally in the compound LiHoxY1−xF4, is related to its phase diagram. In which, the increase in the transverse field takes the system to a quantum critical point (QCP), where there is transition from phase to zero temperature. In the FISG model, spins are written in terms of fermionic operators. This model provides for four distinct states per site, two non-magnetic states |00i and | ↑↓i and two magnetic | ↑ 0i and |0 ↓i. In particular, the objective of the work is to analyze the combined effects of randons transverse and longitudinal fields. In the proposed model, the parameter p is introduced, which controls the fraction of spins on the influence of the transverse field. As a consequence, in addition to allows the alternate between the semi-classical and quantum regimes by adjusting the parameter p, impor tant mechanisms related to the changes in the behavior of non linear susceptibility in the LiHoxY1−xF4 compound are investigated. Through the results obtained, it was observed that only in the presence of a random longitudinal field, ∆/J > 0.00 the divergence is replaced by the maximum in χ3. It is also verified that the temperature T ∗ does not in dicates a phase transition temperature, but a temperature that indicates the presence of a Griffiths phase, in which suggests singularities inside the paramagnetic phase. Another important result was the obtaining of the quantum critical point, a phase transition at T = 0,00. In this case, it was observed that such a point is found only at the quantum limit, when p = 0.00, where all spins are under the influence of the transverse field.