Related papers: Lattice Gas Models with Long Range Interactions
I discuss some of the historical circumstances that drove us to use the lattice as a non-perturbative regulator. This approach has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the…
We analyze phase transitions in the conditional entropy of a sequence caused by a change in the conditional variables. Such transitions happen, for example, when training to learn the parameters of a system, since the transition from the…
We study the $k$-NN hard core lattice gas model in which the first $k$ next nearest neighbor sites of a particle are excluded from occupation by other particles on a two dimensional square lattice. This model is the lattice version of the…
We extend Araki's well-known results on the equivalence of the KMS condition and the variational principle for equilibrium states of quantum lattice systems with short-range interactions, to a large class of models possibly containing…
We study various models of independent particles hopping between energy `traps' with a density of energy barriers $\rho(E)$, on a $d$ dimensional lattice or on a fully connected lattice. If $\rho(E)$ decays exponentially, a true dynamical…
We define a lattice model for rock, absorbers, and gas that makes it possible to examine the flow of gas to a complicated absorbing boundary over long periods of time. The motivation is to deduce the geometry of the boundary from the time…
We consider a model of lattice gas dynamics in the d-dimensional cubic lattice in the presence of disorder. If the particle interaction is only mutual exclusion and if the disorder field is given by i.i.d. bounded random variables, we prove…
The investigation of phase coexistence in systems with multi-component order parameters in finite systems is discussed, and as a generic example, Monte Carlo simulations of the two-dimensional q-state Potts model (q=30) on LxL square…
We study the nuclear liquid-gas phase transition on the basis of a two-component lattice gas model. A Metropolis type of sampling method is used to generate microscopic states in the canonical ensemble. The effective equation of state and…
We consider an off-lattice liquid crystal pair potential in strictly two dimensions. The potential is purely repulsive and short-ranged. Nevertheless, by means of a single parameter in the potential, the system is shown to undergo a…
A new approach to non-extensive thermodynamical systems with non-additive energy and entropy is proposed. The main idea of the paper is based on the statistical matching of the thermodynamical systems with the additive multi-step Markov…
Some dynamical properties of non interacting particles in a bouncer model are described. They move under gravity experiencing collisions with a moving platform. The evolution to steady state is described in two cases for dissipative…
Lattice gas automata with collision rules that violate the conditions of semi-detailed-balance exhibit algebraic decay of equal time spatial correlations between fluctuations of conserved densities. This is shown on the basis of a…
Hard core lattice gas models are minimal models to study entropy driven phase transitions. In the $k$-NN lattice gas, a particle excludes all sites upto the $k$-th next-nearest neighbors from being occupied by another particle. As $k$…
We investigate the entanglement for a model of a particle moving in the lattice (many-body system). The interaction between the particle and the lattice is modelled using Hooke's law. The Feynman path integral approach is applied to compute…
It is discussed how phase transitions of first order (with phase separation and surface tension), continuous transitions and (multi)-critical points can be defined and classified for finite systems from the topology of the energy surface…
We present and discuss the derivation of a nonlinear non-local integro-differential equation for the macroscopic time evolution of the conserved order parameter of a binary alloy undergoing phase segregation. Our model is a d-dimensional…
In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave…
Conserved lattice gas (CLG) models in one dimension exhibit absorbing state phase transition (APT) with simple integer exponents $\beta=1=\nu=\eta$ whereas the same on a ladder belong to directed percolation (DP)universality. We conjecture…
Interaction of particles of many systems can be effectively approximated by multiscale interaction potentials. Such potentials are widely used for investigation of colloidal systems and colloid-polymer mixtures, complex liquids (for…