Farklı istatistiksel modellerde denge dışı faz geçişleri

Non-equilibrium phase transitions of different systems are investigated by several methods. Both of these separate 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 non-equilibrium system are characterized by means of different finite temperatures (Tx and Ty), and also different time-scale constants 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. It is the study in which the full critical surface of this system is reported. Critical exponents of this system are obtained for phase transitions at all limits, and indicate the different universality class properties of the non-equilibrium phase transitions. Secondly, steady state phase transitions of the eight-vertex model, formulated by two interlacing two-dimensional Ising models on square lattices, are studied through four independent Monte Carlo simulations, each with 60 million Monte Carlo steps. To obtain an isotropic system, the spin exchanges are considered to occur within the sublattices. One of the thermal baths coupled to the sublattices has a finite temperature while the other is infinite. The obtained critical exponents are consistent with the equilibrium Ising universality class at this limit. Keywords: Non-Equilibrium Phase Transitions, Renormalization Group Theory, Monte Carlo Simulations, Critical Point, Critical Exponent, Universality.