Exact partition functions of the Ising model on MxN planar lattices with periodic-aperiodic boundary conditions

The Grassmann path integral approach is used to calculate exact partition functions of the Ising model on MxN square (sq), plane triangular (pt) and honeycomb (hc) lattices with periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa) boundary conditions. The partition functions are used to calculate and plot the specific heat, $C/k_B$, as a function of the temperature, $\theta =k_BT/J$. We find that for the NxN sq lattice, $C/k_B$ for pa and ap boundary conditions are different from those for aa boundary conditions, but for the NxN pt and hc lattices, $C/k_B$ for ap, pa, and aa boundary conditions have the same values. Our exact partition functions might also be useful for understanding the effects of lattice structures and boundary conditions on critical finite-size corrections of the Ising model.Comment: 17 pages, 13 Postscript figures, uses iopams.sty, submitted to J. Phys. A: Math. Ge

Shape Effects of Finite-Size Scaling Functions for Anisotropic Three-Dimensional Ising Models

The finite-size scaling functions for anisotropic three-dimensional Ising models of size $L_1 \times L_1 \times aL_1$ ($a$: anisotropy parameter) are studied by Monte Carlo simulations. We study the $a$ dependence of finite-size scaling functions of the Binder parameter $g$ and the magnetization distribution function $p(m)$. We have shown that the finite-size scaling functions for $p(m)$ at the critical temperature change from a two-peak structure to a single-peak one by increasing or decreasing $a$ from 1. We also study the finite-size scaling near the critical temperature of the layered square-lattice Ising model, when the systems have a large two-dimensional anisotropy. We have found the three-dimensional and two-dimensional finite-size scaling behavior depending on the parameter which is fixed; a unified view of 3D and 2D finite-size scaling behavior has been obtained for the anisotropic 3D Ising models.Comment: 6 pages including 11 eps figures, RevTeX, to appear in J. Phys.

Application of exchange Monte Carlo method to ordering dynamics

We apply the exchange Monte Carlo method to the ordering dynamics of the three-state Potts model with the conserved order parameter. Even for the deeply quenched case to low temperatures, we have observed a rapid domain growth; we have proved the efficiency of the exchange Monte Carlo method for the ordering process. The late-stage growth law has been found to be $R(t) \sim t^{1/3}$ for the case of conserved order parameter of three-component system.Comment: 7 pages including 5 eps figures, to appear in New J. Phys. http://www.njp.or

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

Three-dimensional antiferromagnetic q-state Potts models: application of the Wang-Landau algorithm

We apply a newly proposed Monte Carlo method, the Wang-Landau algorithm, to the study of the three-dimensional antiferromagnetic q-state Potts models on a simple cubic lattice. We systematically study the phase transition of the models with q=3, 4, 5 and 6. We obtain the finite-temperature phase transition for q= 3 and 4, whereas the transition temperature is down to zero for q=5. For q=6 there exists no order for all the temperatures. We also study the ground-state properties. The size-dependence of the ground-state entropy is investigated. We find that the ground-state entropy is larger than the contribution from the typical configurations of the broken-sublattice-symmetry state for q=3. The same situations are found for q = 4, 5 and 6.Comment: 9 pages including 9 eps figures, RevTeX, to appear in J. Phys.

Spin Gap in Two-Dimensional Heisenberg Model for CaV4_4O9_9

We investigate the mechanism of spin gap formation in a two-dimensional model relevant to Mott insulators such as CaV$_4$O$_9$. From the perturbation expansion and quantum Monte Carlo calculations, the origin of the spin gap is ascribed to the four-site plaquette singlet in contrast to the dimer gap established in the generalized dimerized Heisenberg model.Comment: 8 pages, 6 figures available upon request (Revtex

Finite-size scaling for the Ising model on the Moebius strip and the Klein bottle

We study the finite-size scaling properties of the Ising model on the Moebius strip and the Klein bottle. The results are compared with those of the Ising model under different boundary conditions, that is, the free, cylindrical, and toroidal boundary conditions. The difference in the magnetization distribution function $p(m)$ for various boundary conditions is discussed in terms of the number of the percolating clusters and the cluster size. We also find interesting aspect-ratio dependence of the value of the Binder parameter at $T=T_c$ for various boundary conditions. We discuss the relation to the finite-size correction calculations for the dimer statistics.Comment: 4 pages including 5 eps figures, RevTex, to appear in Phys. Rev. Let

The Cauchy problem for the 3-D Vlasov-Poisson system with point charges

In this paper we establish global existence and uniqueness of the solution to the three-dimensional Vlasov-Poisson system in presence of point charges in case of repulsive interaction. The present analysis extends an analogeous two-dimensional result by Caprino and Marchioro [On the plasma-charge model, to appear in Kinetic and Related Models (2010)].Comment: 28 page

A Toolkit for Generating Scalable Stochastic Multiobjective Test Problems

Real-world optimization problems typically include uncertainties over various aspects of the problem formulation. Some existing algorithms are designed to cope with stochastic multiobjective optimization problems, but in order to benchmark them, a proper framework still needs to be established. This paper presents a novel toolkit that generates scalable, stochastic, multiobjective optimization problems. A stochastic problem is generated by transforming the objective vectors of a given deterministic test problem into random vectors. All random objective vectors are bounded by the feasible objective space, defined by the deterministic problem. Therefore, the global solution for the deterministic problem can also serve as a reference for the stochastic problem. A simple parametric distribution for the random objective vector is defined in a radial coordinate system, allowing for direct control over the dual challenges of convergence towards the true Pareto front and diversity across the front. An example for a stochastic test problem, generated by the toolkit, is provided