Related papers: Phase Transition in Lattice Surface Systems with G…
We investigate a 3d Ising action which corresponds to a a class of models defined by Savvidy and Wegner, originally intended as discrete versions of string theories on cubic lattices. These models have vanishing bare surface tension and the…
We investigate a model of closed $(d-1)$-dimensional soft-self-avoiding random surfaces on a $d$-dimensional cubic lattice. The energy of a surface configuration is given by $E=J(n_{2}+4k n_{4})$, where $n_{2}$ is the number of edges, where…
We perform numerical simulations of the two and three-dimensional spin systems with competing interaction. They describe the model of random surfaces with linear-gonihedric action.The degeneracy of the vacuum state of this spin system is…
We analyse a new class of statistical systems, which simulate different systems of random surfaces on a lattice. Geometrical hierarchy of the energy functionals on which these theories are based produces corresponding hierarchy of the…
We perform Monte Carlo simulations of a four-dimensional gauge invariant spin system which describes random surfaces with gonihedric action. We develop the analogy between the flat-crumpled phase transition of the lattice surface model and…
We consider a simple lattice model of a topological phase transition in open polymers. To be precise, we study a model of self-avoiding walks on the simple cubic lattice tethered to a surface and weighted by an appropriately defined writhe.…
In a system of interacting thin rigid rods of equal length $2 \ell$ on a two-dimensional grid of lattice spacing $a$, we show that there are multiple phase transitions as the coupling strength $\kappa=\ell/a$ and the temperature are varied.…
A planar square lattice model with 3-d spins interacting with nearest neighbours through a potential -$\epsilon P_4 (cos \theta_{ij})$ is studied by Monte Carlo technique. Lattice sizes from 10$\times$10 to 30$\times$30 are considered for…
The melting transitions of a colloidal lattice confined to a two-dimensional ($2D$) periodic substrate of square symmetry are studied using Monte Carlo simulations. When the strengths of interparticle and particle-substrate interactions are…
The Gonihedric Ising model is a particular case of the class of models defined by Savvidy and Wegner intended as discrete versions of string theories on cubic lattices. In this paper we perform a high statistics analysis of the phase…
We introduce a {\it lattice} version of the Calogero Sutherland model adapted to describe $1/d^2$ pairwise interacting steps with discrete positions on a vicinal surface. The configurational free energy is obtained within a transfer matrix…
We study "random surfaces," which are random real (or integer) valued functions on Z^d. The laws are determined by convex, nearest neighbor, difference potentials that are invariant under translation by a full-rank sublattice L of Z^d; they…
We propose the study of the phase transition in the scalar electroweak theory at finite temperature by a two - step method. It combines i) dimensional reduction to a 3-dimensional {\it lattice\/} theory via perturbative blockspin…
We study vicinal crystal surfaces within the terrace-step-kink model on a discrete lattice. Including both a short-ranged attractive interaction and a long-ranged repulsive interaction arising from elastic forces, we discover a series of…
We consider random lattice triangulations of $n\times k$ rectangular regions with weight $\lambda^{|\sigma|}$ where $\lambda>0$ is a parameter and $|\sigma|$ denotes the total edge length of the triangulation. When $\lambda\in(0,1)$ and $k$…
We have simulated the pure gauge compact QED with fixed boundary conditions, on lattices from $6^4$ to $16^4$. We argue that a lattice with this fixed boundary imposition corresponds actually to a lattice with spherical topology. We have…
We study vicinal crystal surfaces with the terrace-step-kink model on a discrete lattice. Including both a short-ranged attractive interaction and a long-ranged repulsive interaction arising from elastic forces, we discover a series of…
We have used an effective model of ferroelectric PbTiO$_{3}$, which displays a representative soft mode-driven phase transition, to investigate how different features of the potential-energy surface affect the transition temperature $T_{\rm…
We construct a lattice model for a cubic Kondo insulator consisting of one spin-degenerate $d$ and $f$ orbital at each lattice site. The odd-parity hybridization between the two orbitals permits us to obtain various trivial and topological…
The phase behaviour of the Lebwohl-Lasher lattice gas model (one of the simplest representations of a nematogenic fluid) confined in a slab is investigated by means of extensive Monte Carlo simulations. The model is known to yield a first…