相关论文: Low Dimensional Ordering on a Lattice Model

We associate to each unit volume lattice of $\R^d$ the Ising model with bond variables equal to the inverse successive minima of that lattice. This induces the notion of a critical temperature for a random lattice for which integrability…

We study the melting of a moving vortex lattice through numerical simulations with the current driven 3D XY model with disorder. We find that there is a first-order phase transition even for large disorder when the corresponding equilibrium…

The ordinary surface magnetic phase transition is studied for the exactly solvable anisotropic spherical model (ASM), which is the limit D \to \infty of the D-component uniaxially anisotropic classical vector model. The bulk limit of the…

The two-dimensional Ising model is the simplest model of statistical mechanics exhibiting a second order phase transition. While in absence of magnetic field it is known to be solvable on the lattice since Onsager's work of the forties,…

We carry out computer simulations of a simple, two-dimensional off-lattice model that exhibits inverse melting. The monodisperse system comprises core-softened disks interacting through a repulsive square shoulder located inside an…

We develop a fully microscopic, statistical mechanics approach to study phase transitions in Ising systems with competing interactions at different scales. Our aim is to consider orientational and positional order parameters in a unified…

We study dimensional crossover in Ising systems at complex temperatures by comparing three types of system: the infinite isotropic 2D Ising model; the infinite anisotropic 2D Ising model; and Ising ladders with a finite number of legs. In…

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…

The purely plaquette 3d Ising Hamiltonian with the spins living at the vertices of a cubic lattice displays several interesting features. The symmetries of the model lead to a macroscopic degeneracy of the low-temperature phase and prevent…

Conventional gas-liquid phase transitions feature a coexistence line that has a monotonic and positive slope in line with our intuition that cooling always leads to condensation. Here we study the inverse phenomenon, condensation of…

Fluids with competing short range attraction and long range repulsive interactions between the particles can exhibit a variety of microphase separated structures. We develop a lattice-gas (generalised Ising) model and analyse the phase…

We propose a lattice model, in both one- and multidimensional versions, which may give rise to matching conditions necessary for the generation of solitons through the second-harmonic generation. The model describes an array of linearly…

Cold atoms confined in periodic potentials are remarkably versatile quantum systems for implementing simple models prevalent in condensed matter theory. In the current experiment, we realize the 2D Bose-Hubbard model by loading a…

Using grand canonical Monte Carlo (GCMC) simulations, we investigate the isotropic-nematic phase transition for hard rods of size Lx1x1 on a 3D cubic lattice. We observe such a transition for L >= 6. For L = 6, the nematic state has a…

The Lebwohl-Lasher (LL) model is the traditional model used to describe the nematic-isotropic transition of real liquid crystals. In this paper, we develop a numerical study of the temperature behaviour and of finite-size scaling of the…

Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids…

New lattice model for the gradient elasticity is suggested. This lattice model gives a microstructural basis for second-order strain-gradient elasticity of continuum that is described by the linear elastic constitutive relation with the…

We introduce a lattice model for active nematic composed of self-propelled apolar particles,study its different ordering states in the density-temperature parameter space, and compare with the corresponding equilibrium model. The active…

We study a d-dimensional lattice model of diffusing coalescing massive particles, with two parameters controlling deposition and evaporation of monomers. The unique stationary distribution for the system exhibits a phase transition in all…

We introduce a 2-dimensional lattice model of granular matter. We use a combination of proof and simulation to demonstrate an order/disorder phase transition in the model, to which we associate the granular phenomenon of random close…