Non-equilibrium steady state phase transitions of various statistical models

Ankara : The Department of Physics and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Ph. D.) -- Bilkent University, 2013.Includes bibliographical references leaves 79-88.Non-equilibrium phase transitions of a number of systems are investigated by several methods. These systems are in contact with thermal baths with different temperatures and taken to be driven to the non-equilibrium limits by spin exchange (Kawasaki) dynamics. First of all, the criticality of the two-finite temperature spin-1/2 Ising model with a conserved order parameter on a square lattice is studied through a real space renormalization group transformation. The dynamics of the nonequilibrium system are characterized by means of different temperatures (Tx and Ty), and also different time-scale constants, (αx and αy) for spin exchanges in the x and y directions. Based on the RG flows, the critical surface of the system is obtained as a function of these exchange parameters. This is the first study in which the full critical surface displaying various universality classes of this system is reported. Secondly, steady state phase transitions of the eight-vertex model, formulated by two interlaced two-dimensional Ising models on square lattices, are studied through four independent Monte Carlo simulations, each with 60 × 106 Monte Carlo steps on N × N lattices with N = 32, 40, 80, 100. To obtain an isotropic system, the spin exchanges are considered to occur within the sublattices. We observe non-universal behavior for non-equilibrium transitions around the equilibrium transitions, and Ising like behavior when one of the bath temperature becomes very large.Renklioğlu, BaşakPh.D

Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of the s=3/2 Ising model from renormalization-group theory

The spin-3/2 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d=3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d=3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than 14 different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical end points, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The four-state Potts permutation-symmetric subspace is contained in this model