Abstract:
Large-scale simulations on three-dimensional (3D) frustrated anisotropic XY model have been performed to study the nonequilibrium phase transitions of vortex matter in weak random pinning potential in layered superconductors. The first-order phase transition from the moving Bragg glass to the moving smectic is clarified, based on thermodynamic quantities. A washboard noise is observed in the moving Bragg glass in 3D simulations for the first time. It is found that the activation of the vortex loops play the dominant role in the dynamical melting at high drive.

Abstract:
A nonequilibrium Potts-like model with $q$ absorbing states is studied using Monte Carlo simulations. In two dimensions and $q=3$ the model exhibits a discontinuous transition. For the three-dimensional case and $q=2$ the model exhibits a continuous, transition with $\beta=1$ (mean-field). Simulations are inconclusive, however, in the two-dimensional case for $q=2$. We suggest that in this case the model is close to or at the crossing point of lines separating three different types of phase transitions. The proposed phase diagram in the $(q,d)$ plane is very similar to that of the equilibrium Potts model. In addition, our simulations confirm field-theory prediction that in two dimensions a branching-annihilating random walk model without parity conservation belongs to the directed percolation universality class.

Abstract:
Quenched disorder affects significantly the behavior of phase transitions. The Imry-Ma-Aizenman-Wehr-Berker argument prohibits first-order or discontinuous transitions and their concomitant phase coexistence in low-dimensional equilibrium systems in the presence of random fields. Instead, discontinuous transitions become rounded or even continuous once disorder is introduced. Here we show that phase coexistence and first-order phase transitions are also precluded in nonequilibrium low-dimensional systems with quenched disorder: discontinuous transitions in two-dimensional systems with absorbing states become continuous in the presence of quenched disorder. We also study the universal features of this disorder-induced criticality and find them to be compatible with the universality class of the directed percolation with quenched disorder. Thus, we conclude that first-order transitions do not exist in low-dimensional disordered systems, not even in genuinely nonequilibrium systems with absorbing states.

Abstract:
nonequilibrium kinetic ising models evolving under the competing effect of spin flips at zero temperature and kawasaki-type spin-exchange kinetics at infinite temperature t are investigated here in one dimension from the point of view of phase transition and critical behaviour. branching annihilating random walks with an even number of offspring (on the part of the ferromagnetic domain boundaries), is a decisive process in forming the steady state of the system for a range of parameters, in the family of models considered. a wide variety of quantities characterize the critical behaviour of the system. results of computer simulations and of a generalized mean field theory are presented and discussed.

Abstract:
Nonequilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and Kawasaki-type spin-exchange kinetics at infinite temperature T are investigated here in one dimension from the point of view of phase transition and critical behaviour. Branching annihilating random walks with an even number of offspring (on the part of the ferromagnetic domain boundaries), is a decisive process in forming the steady state of the system for a range of parameters, in the family of models considered. A wide variety of quantities characterize the critical behaviour of the system. Results of computer simulations and of a generalized mean field theory are presented and discussed.

Abstract:
I review in this chapter several classes of quantum phase transitions that occur in quasi-one dimensional systems. I start by examining the simple case of coupled spin chains and ladders, then move to the case of bosons, and finally deal with the more complicated and still largely open case of fermions.

Abstract:
We have previously studied properties of a one-dimensional potential with $N$ equally spaced identical barriers in a (fixed) finite interval for both finite and infinite $N$. It was observed that scattering and spectral properties depend sensitively on the ratio $c$ of spacing to width of the barriers (even in the limit $N \to \infty$). We compute here the specific heat of an ensemble of such systems and show that there is critical dependence on this parameter, as well as on the temperature, strongly suggestive of phase transitions.

Abstract:
We address the question of the quantitative relationship between thermodynamic phase transitions and topological changes in the potential energy manifold analyzing two classes of one dimensional models, the Burkhardt solid-on-solid model and the Peyrard-Bishop model for DNA thermal denaturation, both in the confining and non-confining version. These models, apparently, do not fit [M.Kastner, Phys. Rev. Lett. 93, 150601 (2004)] in the general idea that the phase transition is signaled by a topological discontinuity. We show that in both models the phase transition energy v_c is actually non-coincident with, and always higher than, the energy v_theta at which a topological change appears. However, applying a procedure already successfully employed in other cases as the mean field phi^4 model, i.e. introducing a map M(v)=v_s from levels of the energy hypersurface V to the level of the stationary points "visited" at temperature T, we find that M(v_c)=v_theta. This result enhances the relevance of the underlying stationary points in determining the thermodynamics of a system, and extends the validity of the topological approach to the study of phase transition to the elusive one-dimensional systems considered here.

Abstract:
The effects of locally broken spin symmetry are investigated in one dimensional nonequilibrium kinetic Ising systems via computer simulations and cluster mean field calculations. Besides a line of directed percolation transitions, a line of transitions belonging to N-component, two-offspring branching annihilating random-walk class (N-BARW2) is revealed in the phase diagram at zero branching rate. In this way a spin model for N-BARW2 transitions is proposed for the first time.

Abstract:
Microcanonical analysis is a powerful method for studying phase transitions of finite-size systems. This method has been used so far only for studying phase transitions of equilibrium systems, which can be described by microcanonical entropy. I show that it is possible to perform microcanonical analysis of a nonequilibrium phase transition, by generalizing the concept of microcanonical entropy. One-dimensional asymmetric diffusion process is studied as an example where such a generalized entropy can be explicitly found, and the microcanonical method is used to analyze a nonequilibrium phase transition of a finite-size system.