These lecture notes give a basic introduction to the physics of phase transitions under non-equilibrium conditions. The notes start with a general introduction to non-equilibrium statistical mechanics followed by four parts. The first one discusses the universality class of directed percolation,...

The standard Potts model is investigated in the framework of nonextensive statistical mechanics. We performed Monte Carlo simulations on two-dimensional lattices with linear sizes ranging from 16 to 64 using the Metropolis algorithm, where the classical Boltzmann–Gibbs transition probabilities...

Discovery of the anomalous generation and extinction of crystal nuclei in nonequilibrium supercooled liquids reflects essentially the effects of the real heterogeneous structure and its irreversible relaxation on the stability of the nucleus. The kinetic model involving one order parameter was...

We studied the coverage dependence of the differential heat of adsorption in the presence of an order–disorder phase transition, by employing theoretical mean-field and quasi-chemical approaches and Monte Carlo simulation, in the framework of the lattice-gas model. For a square lattice, with...

The phase transition of a fluid adsorbed in a heterogeneous system is studied within a mean-field approach to the lattice gas model with quenched impurities. Despite the different origin of the heterogeneity (spatial variation of binding energy or fluid coordination numbers), the fluid can...

Phase transitions, ubiquitous in condensed matter physics, are encountered in computer science too. The existence of critical phenomena has deep consequences on computational complexity, that is the resolution times of various optimization or decision problems. Concepts and methods borrowed from...

In this paper, we consider a time-headway model, introduced in Ref. [Physica A 296 (2001) 320], for buses on a bus route. By including a simple no-passing rule, we are able to enumerate and study the unstable modes of a homogeneous system. We then discuss the application of the model to...

Dynamic phase transitions in a two-dimensional traffic flow model defined on a decorated square-lattice are studied numerically. The square-lattice point and the decorated site denote intersections and roads, respectively. In the present model, a car has a finite deterministic path between the...

We apply the Ising model in a transverse field to analyse the properties of KH2PO4/KD2H2PO4 superlattice using the effective field theory with a probability distribution technique. The dielectric-susceptibility and the macroscopic pyroelectric coefficient are calculated for possible comparison...

It has been rigorously proved that the ground state of interacting quantum rotors in two dimensions exhibits the magnetic long-range order in the ferromagnetic case. The assumptions are that the interaction is between nearest neighbors and it is strong enough, and that rotors are sufficiently...