Study Of The Thermodynamics, Phase Transitions And Critical Phenomena On Low-dimensional Confining Systems

The study of two-dimensional XY model has been attracting many interests for recent years. The ground states of a large class of two-dimensional classical frustrated XY models have the particularity to exhibit both continuous and discrete degeneracy simultaneously. These XY-type models are often used for describing the superfluid systems and the superconducting array of Josephson junctions in the literatures. It has been found that the model inherent symmetry is associated with the two-types of chirality ordering, characterizing phase transitions, namely, the so-called Kosterliz-Thouless (KT) and Ising transitions. Nevertheless, the entanglements between the orders considerably complicate the theoretical analysis due to spin interactions in a magnetic sample. For example, the spin interactions, originated from Dzyaloshinskii and Moriya, significantly describe a class of the combination of superexchanging spin-orbital interactions. The Dzyaloshinskii-Moriya (DM) interactions are linear in spin-orbital coupling, leading to magnetic disorder effects. In general, the DM interactions are antisymmetric since the chirality, lead to special spin configurations. On the appearance of the DM interactions, magnetic systems usually display the complex phase transitions in behaviors. In this sense, Monte Carlo (MC) simulations provide us a powerful tool for the study of such complicate systems. To carry out Monte Carlo simulations, the central duty is to explore the high-resolution and fast speed MC algorithms.In this thesis a new combination Monte Carlo technique of the Metropolis algorithm and the Swendsen-Wang (SW) cluster algorithm is proposed. Upon application of new MC technique, the thermodynamic properties, phase transitions, critical phenomena and the dynamic correlation functions of spin in a generalized XY model with the DM interactions are simulated. We find that there is new competition between the chiral order and the ferromagnetic order with the change of the DM strength. When the DM strength is weak, the critical temperature decreases little with the increasing of the DM strength and the plats appear in the plots of the magnetization variation with the temperature. So the system is ferromagnetic. When the DM strength is strong, the plat disappears and the magnetization decreases even it is less than the high temperature magnetization. These indicate the strong chiral order restrains the ferromagnetic order and the system is more stable. The spin dynamic correlation functions are computed by using the new combination algorithm and the Metropolis algorithm. The result shows that the speed of the combination algorithm is four times of the Metropolis algorithm.New vortex excitations are reduced by the DM interactions and can be interpreted as the mechanism of the magnetization and the ferromagnetic order for the relevant strong DM interaction. To clarify this issue, we further research the chirality and the spin structure of the square and triangular lattices. We find that the vortices exhibit the period along the orientation vertical to the diagonal of lattices. The period is related to the DM strength and the period is shorter as the DM strength is stronger. The critical properties of the chiral system are studied by using the Binder cumulant. We find that the critical temperature TC≈0.92 without the DM interactions by computing the plot of the Binder cumulant variation to the temperature in different lattices size system. There is the scaling about the temperature critical indexη=1/4 in the KT transitions. We can see that the critical temperature decreases with the increasing of the DM strength.The investigation of the spin dynamic indicates that the vortices coexist with spin wave as the temperature is not too low. The main contribution to the thermal conductance comes from the spin wave excitation. However the thermal conductance is determined by the specific heat and the dynamic correlation time. In the coexistence domain KT transitions are correlative to the spin glass theory. The critical temperature is propotionable to DM strength.Finally, we are interested in quantum thermal transport. We derive a kind of Landauer-Buttiker(LB) formula about the quantum thermal conductance by using nonequilibrium Green's function method, present the theory model about extremely cold dielectric chains and study the quantum thermal conductance of the low-lying excited mode. We find that the thermal conductance undergoes an anomalous transition due to quasiparticle excitations. The theoretical prediction describes well the nonintegral effect of the thermal conductance in the thermal conductance measurement.