A new graphical method is developed to calculate the critical temperature of 2and 3-dimensional Ising models as well as that of the 2-dimensional Potts models. This method is based on the transfer matrix method and using the limited lattice for the calculation. The reduced internal energy per site has been accurately calculated for different 2-D Ising and Potts models using different size-limit...

in this paper we investigate the effect of a random transverse field, distributed according to a trimodal distribution, on the phase diagram and magnetic properties of a two-dimensional lattice (square with z=4),  ferromagnetic ising system consisting of magnetic atoms with spin-1. this study is done using the effectivefield theory (eft) with correlations method. the equations are derived using...

We study the correction-to-scaling exponents for the two-dimensional selfavoiding walk, using a combination of series-extrapolation and Monte Carlo methods. We enumerate all self-avoiding walks up to 59 steps on the square lattice, and up to 40 steps on the triangular lattice, measuring the mean-square end-to-end distance, the mean-square radius of gyration and the mean-square distance of a mon...

In the present paper a novel structure for optical channel drop filter (CDF) based on photonic crystal ring resonator with circular core has been proposed. In order to design the proposed CDF, the plan wave expansion (PWE) method is applied for calculation of band structure and photonic band gap while the transmission characteristics of proposed CDF have been calculated using the finite differe...

2014 The two-dimensional random Boolean networks suggested by Kauffman have a transition to chaos. We find by Monte Carlo simulation the periods of the limit cycles, both for each site as well as for the lattice as a whole, at the transition point and away from it, for the square lattice. The triangular lattice seems to have the same fractal dimensions as the square lattice. J. Physique 48 (198...

We construct, in discrete two-component systems with cubic nonlinearity, stable states emulating Skyrmions of the classical field theory. In the two-dimensional case, an analog of the baby Skyrmion is built on the square lattice as a discrete vortex soliton of a complex field [whose vorticity plays the role of the Skyrmion's winding number (WN)], coupled to a radial "bubble" in a real lattice f...

A random tiling of rectangles and triangles displaying a decagonal phase is solved by Bethe Ansatz. Analogously to the solutions of the dodecagonal square triangle and the octagonal rectangle triangle tiling an exact expression for the maximum of the entropy is found. PACS numbers: 05.20.-y, 05.50.+q, 04.20.Jb, 61.44.Br Short title: Solution of a decagonal random tiling February 1, 2008 † Elect...

A cluster for the octagonal square-rhombus tiling is presented, which has the property that among all tilings completely covered by the cluster the perfectly quasiperiodic and eightfold symmetric ones have the highest cluster density. Since on these eightfold symmetric tilings there is considerable overlap of clusters, it seems likely that these tiling have the highest cluster density even amon...

We give an explicit formula for the mean square displacement of random walk on d -dimensional Manhattan lattice after n steps, all and dimensions ≥ 2 .

Consider the square lattice Z with vertices at points with integer-valued coordinates in R = {(x1, x2)| xk ∈ R, k = 1, 2} and complex (or real) scalar fields u on the lattice Z, u : Z → C, that are defined by their values ui1i2 , ui1i2 ∈ C, at each vertex of the lattice with the coordinates (i1, i2), ik ∈ Z, k = 1, 2. Consider a class of two-dimensional discrete equations on the lattice Z for t...