3,405 research outputs found
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, , as a function of the temperature, . We find that
for the NxN sq lattice, for pa and ap boundary conditions are different
from those for aa boundary conditions, but for the NxN pt and hc lattices,
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 (: anisotropy parameter) are
studied by Monte Carlo simulations. We study the dependence of finite-size
scaling functions of the Binder parameter and the magnetization
distribution function . We have shown that the finite-size scaling
functions for at the critical temperature change from a two-peak
structure to a single-peak one by increasing or decreasing 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 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 CaVO
We investigate the mechanism of spin gap formation in a two-dimensional model
relevant to Mott insulators such as CaVO. 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 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
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
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