An Ising spin - S model on generalized recursive lattice

The Ising spin - S model on recursive p - polygonal structures in the external magnetic field is considered and the general form of the free energy and magnetization for arbitrary spin is derived. The exact relation between the free energies on infinite entire tree and on its infinite "interior" is obtained.Comment: 9 pages, 1 figure, to be published in Physica

Quark-Antiquark Energy Density Function applied to Di-Gauge Boson Production at the LHC

In view of the start up of the 14 TeV pp Large Hadron Collider the quark anti-quark reactions leading to the final states W^+W^-, W^+-Z^0 and Z^0Z^0 are studied, in the frame workn of the Standard Model (SM), using helicity amplitudes. The differential and total cross sections are first evaluated in the parton-parton center of mass system. They are then transformed to their expected behavior in pp collisions through the parton-parton Energy Density Functions which are here derived from the known Parton Density Functions of the proton. In particular the single and joint longitudinal polarizations of the final state di-bosons are calculated. The effect on these reactions from the presence of s-channel heavy vector bosons, like the W' and Z', are evaluated to explore the possibility to utilize the gauge boson pair production as a probe for these 'Beyond the SM' phenomena.Comment: 15 pages and 8 figures

Non-Local Finite-Size Effects in the Dimer Model

We study the finite-size corrections of the dimer model on ∞ × N square lattice with two different boundary conditions: free and periodic. We find that the finite-size corrections depend in a crucial way on the parity of N, and show that, because of certain non-local features present in the model, a change of parity of N induces a change of boundary condition. Taking a careful account of this, these unusual finite-size behaviours can be fully explained in the framework of the c = -2 logarithmic conformal field theory

Boundary conditions and amplitude ratios for finite-size corrections of a one-dimensional quantum spin model

We study the influence of boundary conditions on the finite-size corrections of a one-dimensional (1D) quantum spin model by exact and perturbative theoretic calculations. We obtain two new infinite sets of universal amplitude ratios for the finite-size correction terms of the 1D quantum spin model of $N$ sites with free and antiperiodic boundary conditions. The results for the lowest two orders are in perfect agreement with a perturbative conformal field theory scenario proposed by Cardy [Nucl. Phys. B {\bf 270}, 186 (1986)].Comment: 15 page

Simplified Transfer Matrix Approach in the Two-Dimensional Ising Model with Various Boundary Conditions

A recent simplified transfer matrix solution of the two-dimensional Ising model on a square lattice with periodic boundary conditions is generalized to periodic-antiperiodic, antiperiodic-periodic and antiperiodic-antiperiodic boundary conditions. It is suggested to employ linear combinations of the resulting partition functions to investigate finite-size scaling. An exact relation of such a combination to the partition function corresponding to Brascamp-Kunz boundary conditions is found.Comment: Phys.Rev.E, to be publishe

Chaos in the Z(2) Gauge Model on a Generalized Bethe Lattice of Plaquettes

We investigate the Z(2) gauge model on a generalized Bethe lattice with three plaquette representation of the action. We obtain the cascade of phase transitions according to Feigenbaum scheme leading to chaotic states for some values of parameters of the model. The duality between this gauge model and three site Ising spin model on Husimi tree is shown. The Lyapunov exponent as a new order parameter for the characterization of the model in the chaotic region is considered. The line of the second order phase transition, which corresponds to the points of the first period doubling bifurcation, is also obtained.Comment: LaTeX, 7 pages, 4 Postscript figure

Chaotic Repellers in Antiferromagnetic Ising Model

For the first time we present the consideration of the antiferromagnetic Ising model in case of fully developed chaos and obtain the exact connection between this model and chaotic repellers. We describe the chaotic properties of this statistical mechanical system via the invariants characterizing a fractal set and show that in chaotic region it displays phase transition at {\it positive} "temperature" $\beta_c = 0.89$. We obtain the density of the invariant measure on the chaotic repeller.Comment: LaTeX file, 10 pages, 4 PS figurs upon reques

Equivalence between non-bilinear spin-SS Ising model and Wajnflasz model

We propose the mapping of polynomial of degree 2S constructed as a linear combination of powers of spin-$S$ (for simplicity, we called as spin-$S$ polynomial) onto spin-crossover state. The spin-$S$ polynomial in general can be projected onto non-symmetric degenerated spin up (high-spin) and spin down (low-spin) momenta. The total number of mapping for each general spin-$S$ is given by $2(2^{2S}-1)$. As an application of this mapping, we consider a general non-bilinear spin-$S$ Ising model which can be transformed onto spin-crossover described by Wajnflasz model. Using a further transformation we obtain the partition function of the effective spin-1/2 Ising model, making a suitable mapping the non-symmetric contribution leads us to a spin-1/2 Ising model with a fixed external magnetic field, which in general cannot be solved exactly. However, for a particular case of non-bilinear spin-$S$ Ising model could become equivalent to an exactly solvable Ising model. The transformed Ising model exhibits a residual entropy, then it should be understood also as a frustrated spin model, due to competing parameters coupling of the non-bilinear spin-$S$ Ising model

Universal relations in the finite-size correction terms of two-dimensional Ising models

Quite recently, Izmailian and Hu [Phys. Rev. Lett. 86, 5160 (2001)] studied the finite-size correction terms for the free energy per spin and the inverse correlation length of the critical two-dimensional Ising model. They obtained the universal amplitude ratio for the coefficients of two series. In this study we give a simple derivation of this universal relation; we do not use an explicit form of series expansion. Moreover, we show that the Izmailian and Hu's relation is reduced to a simple and exact relation between the free energy and the correlation length. This equation holds at any temperature and has the same form as the finite-size scaling.Comment: 4 pages, RevTeX, to appear in Phys. Rev. E, Rapid Communication