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Statistical mechanics of a disordered system of cars on a single-lane road is developed. Behaviour of cars is defined by conditional probability of car velocity depending on the distance and velocity of the car ahead. A system consisting of different cars is modelled by a system of two types of cars differing in maximal velocity or efficiency of brakes. Starting from conditional probabilities and using principle of maximum entropy, probability densities of car velocities and headways are calculated. It is shown that the first-order phase transition between free flow and congested traffic may be driven by number of fast cars in a system of slow cars, and, as a rule, admixture of cars of superior qualities does not increase but decreases the total flow. In the system of cars with poor brakes platoons of cars of the same velocity are formed. They are dissolved by a small addition of cars with good brakes. Application of principle of maximum entropy was justified by comparing the results with steady state properties of an equivalent kinetic model., Comment: 17 pages, 11 figures

Statistical mechanics of a small system of cars on a single-lane road is developed. The system is not characterized by a Hamiltonian but by a conditional probability of a velocity of a car for the given velocity and distance of the car ahead. Distribution of car velocities for various densities of a group of cars are derived as well as probabilities of density fluctuations of the group for different velocities. For high braking abilities of cars free-flow and congested phases are found. Platoons of cars are formed for system of cars with inefficient brakes. A first order phase transition between free-flow and congested phase is suggested., Comment: 12 pages, 6 figures, presented at TGF, Paris, 2007

A system of identical cars on a single-lane road is treated as a microcanonical and canonical ensemble. Behaviour of the cars is characterized by the probability of car velocity as a function of distance and velocity of the car ahead. The calculations a performed on a discrete 1D lattice with discrete car velocities. Probability of total velocity of a group of cars as a function of density is calculated in microcanonical approach. For a canonical ensemble, fluctuations of car density as a function of total velocity is found. Phase transitions between free and jammed flow for large deceleration rate of cars and formation of queues of cars with the same velocity for low deceleration rate are described., Comment: 13 pages, 8 figures, submitted to Physica A

An effective-field method for caculation of thermodynamic properties of three-dimensional lattice spin models is developed. It is applied to the ANNNI model on the simple cubic lattice. The phase diagram of the model, consisting of a large number of commensurate phases and of an incommensurate phase, is calculated, confirming the results of previous approaches. The phase transition lines for a number of commensurate structures are localized, and a strong evidence for absence of the direct phase transition between commensurate phases and the disordered phase is found., Comment: 8 pages, 8 figures, references removed and replaced

The classical two-dimensional anisotropic triangular nearest-neighbor Ising (ATNNI) model is studied by the density matrix renormalization group (DMRG) technique when periodic boundary conditions are imposed. Applying the finite-size scaling to the DMRG results a commensurate-disordered (C-D) phase transition line as well as temperature and magnetic critical exponents are calculated. We conclude that the (C-D) phase transition in the ATNNI model belongs to the same universality class as the ordered-disordered phase transition of the Ising model., Comment: 6 pages, 4 figures

The Density Matrix Renormalization Group (DMRG) method with periodic boundary conditions is introduced for two dimensional classical spin models. It is shown that this method is more suitable for derivation of the properties of infinite 2D systems than the DMRG with open boundary conditions despite the latter describes much better strips of finite width. For calculation at criticality, phenomenological renormalization at finite strips is used together with a criterion for optimum strip width for a given order of approximation. For this width the critical temperature of 2D Ising model is estimated with seven-digit accuracy for not too large order of approximation. Similar precision is reached for critical indices. These results exceed the accuracy of similar calculations for DMRG with open boundary conditions by several orders of magnitude., Comment: REVTeX format contains 8 pages and 6 figures, submitted to Phys. Rev. B

A modified density matrix renormalization group (DMRG) method is introduced and applied to classical two-dimensional models: the anisotropic triangular nearest- neighbor Ising (ATNNI) model and the anisotropic triangular next-nearest-neighbor Ising (ANNNI) model. Phase diagrams of both models have complex structures and exhibit incommensurate phases. It was found that the incommensurate phase completely separates the disordered phase from one of the commensurate phases, i. e. the non-existence of the Lifshitz point in phase diagrams of both models was confirmed., Comment: 14 pages, 14 figures included in text, LaTeX2e, submitted to PRB, presented at MECO'24 1999 (Wittenberg, Germany)

A new approach to derivation of various effective-field approximation for lattice spin models is presented. It is shown that it can give a number of methods, including the DMRG method, that can be used to find generally inhomogeneous solutions of 2D classical lattice problems. A method, closely related the DMRG method but without necessity to perform any renormalization, is derived, yielding results practically not different from the DMRG ones. The matrix-product wave function of Rommer and \"Ostlund can be constructed from the output of the method. The computational costs of all the derived methods are smaller than those of the DMRG. Most of the results are applicable to the 1D quantum systems, as well., Comment: 13 pages, 1 figure in text; plainTex, submitted to Acta Physica Slovaca, presented at MECO'24-1999, Wittenberg Abstract changed, discussion and references added

An anisotropic spin model on a triangular semiinfinite lattice with ferromagnetic nearest-neighbour interactions and one antiferromagnetic next-nearest-neighbour interaction is investigated by the cluster transfer-matrix method. A phase diagram with <2> antiphase, ferromagnetic, incommensurate, and disordered phase is obtained. The bulk uniaxial incommensurate structure modulated in the direction of the competing interactions is found between the <2> antiphase and the disordered phase. The incommensurate structure near the surface with free and <2> boundary condition is studied at different temperatures. Paramagnetic damping at the surface and enhancement of the incommensurate structure in the subsurface region at high temperatures and a new subsurface incommensurate structure modulated in two directions at low temperatures are found., Comment: 13 pages, plainTex, 11 figures, paper submitted to J. Phys. A