Real-space renormalization-group transformation for finite thickness ising systems

The real-space renormalization group transformation based on the cumulant expansion is modified for systems with free-surface boundary conditions. Free energies and heat capacities of ferromagnetic strips (n x ∞) and slabs (n x ∞ x ∞) are determined over a wide temperature range. The critical or pseudocritical behavior approaches the bulk limit as n → ∞ according to a simple power law, [T_c(n) ? T_c (∞)] ∞n^?λ it is verified that the shift exponent λ is equal to the reciprocal of the critical length exponent.     

Percolation cluster algorithm and scaling behaviour in the 4-dimensional ising model

The scaling behaviour of renormalized quantities and the validity of renormalized perturbation theory is tested numerically in the symmetric phase of the 4-dimensional Ising model. The high-precision Monte Carlo calculation is based on an efficient percolation cluster algorithm.     

Correlation between charged-particle multiplicities and pseudo-rapidity distributions in hydrodynamical cluster model

It is shown that the correlation between charged-particle multiplicities and pseudo-rapidity distributions, such as the one observed in ISR as well as in recent \(\bar pp\) collider experiments may well be understood in terms of the previously studied hydrodynamically-expanding large-cluster model.     

Exact renormalization transformation for the one-dimensional ising model with finite range interaction

The transfer matrix formalism is employed in order to construct the exact renormalization transformation for the one-dimensional Ising model with finite range interaction. The method is applied to the nearest-neighbour model and to the next nearest-neighbour model.     

Contribution to the theory of mixed ising spin systems

An effective-field theory of mixed spin—1/2 and spin-1 Ising system with random bond and crystal-field interactions is developed. The general expressions for evaluating the thermodynamic quantities are obtained. In the last section, transition temperature and tricritical behavior are examined for the mixed ferromagnetic spin system withz=3, wherez is the coordination number. The obtained results are reasonable in comparison with exact and approximate ones. Owing to the simplicity, the present method can be applied to a wide class of the random systems.     

Lifshitz points in ising systems

Phase diagrams of Ising systems with competing interactions are calculated using (a) the method of Müller-Hartmann and Zittartz to determine the transition temperature via the vanishing of an interface free energy (b) a Migdal-Kadanoff bond-moving scheme and (c) Monte Carlo simulations. It is shown that in two-dimensional Ising systems a uniaxial Lifshitz point can exist at non-zero temperatures, whereas the lower critical dimensiond _l for a Lifshitz point in a system with identical competing interactions along each of its cartesian axis isd _l 2.     

Block spin techniques applied to the ising model

A detailed study of the critical behaviour of the Ising model in 1+1 and 2+1 dimensions is made using an approximate real space renormalization transformation which involves block spins. The critical indices α, β, η, and ν are calculated and compared with previous results, as is the critical couplingy _c. The method is shown to respect one of the scaling relations, and in 1+1D some exact results are reproduced (y _c=1, ν=1).     

Metastability in the two-dimensional ising model

Metastability in the Ising model is studied in two ways. In a dynamical Monte Carlo model, metastable magnetization and lifetime are measured for various magnetic fields and low temperatures. Following up a proposed relation between analytic continuation of transfer matrix eigenvalues and metastability, transfer matrix eigenvalues are studied. We examine the extent to which these approaches agree. The Monte Carlo data also provide quantitative support for the critical droplet model for decay.     

Mutual information of ising systems

We obtain the mutual information of Ising systems, which shows singular behavior near the critical point. We connect the mutual information with the magnetization and the correlation function. The mutual information is a suitable measure for the critical behavior of Ising systems.     

Kinetic ising model study of phase separation in binary alloys

The decomposition of binary alloys after a sudden quench below the critical temperature of unmixing is studied on a microscopic basis, using a stochastic model analog to the Kawasaki spin exchange Ising model. For interactions of long range the model reduces to the standard phenomenological equation. We relate this nonlinear equation to our recent treatment of the time-dependent Ginzburg-Landau theory, and calculate the nonequilibrium relaxation functions. For interactions of short range we present some computer simulations. As example, we treat a 55×55 square lattice, with a gradient in the chemical potential. Details are given for the relaxation process, which is a coarsening at the initial stage of the decomposition, while later the gradient produces a more macroscopic phase separation.     

Large deviations for the 2D ising model: A lower bound without cluster expansions

We show that a lower large-deviation bound for the block-spin magnetization in the 2D Ising model can be pushed all the way forward toward its correct Wulff value for all >_c.     

Application of the real space dynamic renormalization group method to the one-dimensional kinetic ising model

We apply the recently developed real space dynamic renormalization group method to the one-dimensional kinetic Ising model. We show how one can develop block spin methods that lead to recursion relations for the space and time dependent correlation functions that correspond to the observables for this system. We point out the importance of carefully choosing the appropriate parameters governing the behavior of individual blocks of spins and the necessity of worrying about the high temperature properties of the temperature recursion relations if one is to obtain the proper exponential decay of correlation functions at large distances away from the critical point at zero temperature. We systematically investigate the accuracy of our approximate recursion relations for various correlation functions by checking them against the known exact results. Our simple methods work surprisingly well over a wide range of temperatures, wavenumbers and frequencies.     

Bounds to the wave-vector dependent susceptibility of the ising model

It is shown that rigorous upper and lower bounds to the wave-vector dependent susceptibility of the Ising Model are obtained either when an upper bound to the spin pair correlation function and a lower bound to the susceptibility at zero wave-vector are given, or when a lower bound to the former and an upper bound to the latter are given. An example of the numerical computation of the bounds is presented for the Ising model on the sc lattice.     

Finite cluster approximation for bond and site dilution transverse ising model on square lattice

The critical behaviour of the bond and site dilution transverse Ising model on a square lattice with spin-1/2 is investigated within the framework of the finite cluster approximation (FCA). The phase diagrams, critical temperature, critical transverse field and percolation threshold are given. The FCA method is conceptually as simple as an ordinary mean field approximation (MFA) but gives much better results.     

Phase diagram of the half-infinite ising model

The phase diagram is analyzed rigorously, and in particular the wetting transition is discussed.     

Dynamics of magnetization of frustrated ising systems

The dynamics of magnetization in triangle lattices of the Ising chains has been investigated in terms of the Glauber theory. The results of three-dimensional numerical simulation of the magnetic structure and magnetization curves of Ca₃Co₂O₆ are presented. The structures of the low-temperature and high-temperature phases differ significantly: the false frustrated low-temperature phase is transformed into a partially disordered antiferromagnetic honeycomb structure. Two additional magnetization steps at low temperatures are formed at the expense of the domain structure and the ferrimagnetic phase. All fundamental hypotheses used in terms of the two-dimensional model have found their confirmation during the three-dimensional simulation.     

Higher-order correlation functions of the planar ising model

A method of calculating the asymptotic behaviour of the higher-order correlation functions for large distances is proposed for the planar Ising model in the absence of a magnetic field. The three-point correlation functions composed of a spin operator or of energy-density operators are considered. The asymptotic behaviour of the correlation functions for distances R ? R_c (where R_c is the correlation radius) is determined. It is shown that the asymptotic behaviour of the correlation functions for large distances does not depend on the choice of operators. The asymptotic behaviour of the correlation functions in which two operators are relatively close to one another is considered near the critical point. The results which we obtained are compared with the predictions of the scaling laws and operator algebra.