Uma proposta de modelo de acoplamento spin-rede anisotrópico

Abstract

This thesis’s main focus is to propose a suitable model for the study of spin systems that addresses a spin-lattice coupling capable of respecting the symmetry of the crystal lattice and simultaneously allowing for the evaluation of the effects that the vibration of this lattice, established in a preferred direction, has on the spin interactions. To achieve this objective, as a starting point, we adjusted and generalized a proposal established in my master’s thesis for the study of Ising-type spin systems. In this thesis, after formulating a general representation of the model for spins of this type, we adopt the triangular lattice as the object of application. This combination establishes a rotational anisotropy for the spin interactions that is derived from the association of the lattice’s preferred direction of vibration with a parameter recognized in the model as Ja. This parameter measures the degree of interaction between the lattice and the spins. In short, when Ja > 0, the system will favor the interaction of spins located along the lattice’s preferred direction of vibration. However, when Ja < 0, interactions outside this preferred direction will be favored up to a certain critical Ja value. The method chosen to evaluate the entire spin dynamics under these conditions was an entropic sampling technique whose simulation approach is linked to the WangLandau algorithm. Although we provided a comprehensive description of the system for both Ja conditions, the simulation results were exclusively dedicated to the Ja < 0 case. With this strategy, we were able to direct our study to evaluate the system’s behavior under specific circumstances of interest, as determined by the phase diagram from the low-temperature to the high-temperature regime. This analysis prompted us to more thoroughly investigate the system’s behavior at Ja = −1.0, Ja = −3.0, and in the region around Ja = −4.0, where the system reaches a regime of maximum frustration. For each of these conditions, we were able to calculate some basic thermodynamic properties of interest, such as the system’s energy, specific heat, magnetization, and magnetic susceptibility. These data, along with the various simulations performed for various lattice sizes chosen based on this proposal, also helped us identify the existence of exotic phases associated with the point of maximum frustration and its surroundings. Furthermore, we were also able to evaluate the system’s behavior at criticality, where we calculated several critical exponents using finite-size scaling theory. This allowed us to argue for the occurrence of conventional phase transitions (such as second-order transitions) and unconventional phase transitions (such as the weak first-order transition), in addition to the likely universality class associated with specific points on the phase diagram.