551 research outputs found
Vertex Models and Random Labyrinths: Phase Diagrams for Ice-type Vertex Models
We propose a simple geometric recipe for constructing phase diagrams for a
general class of vertex models obeying the ice rule. The disordered phase maps
onto the intersecting loop model which is interesting in its own right and is
related to several other statistical mechanical models. This mapping is also
useful in understanding some ordered phases of these vertex models as they
correspond to the polymer loop models with cross-links in their vulcanised
phase.Comment: 8 pages, 6 figure
Ensemble dependence in the Random transverse-field Ising chain
In a disordered system one can either consider a microcanonical ensemble,
where there is a precise constraint on the random variables, or a canonical
ensemble where the variables are chosen according to a distribution without
constraints. We address the question as to whether critical exponents in these
two cases can differ through a detailed study of the random transverse-field
Ising chain. We find that the exponents are the same in both ensembles, though
some critical amplitudes vanish in the microcanonical ensemble for correlations
which span the whole system and are particularly sensitive to the constraint.
This can \textit{appear} as a different exponent. We expect that this apparent
dependence of exponents on ensemble is related to the integrability of the
model, and would not occur in non-integrable models.Comment: 8 pages, 12 figure
Invaded cluster algorithm for equilibrium critical points
A new cluster algorithm based on invasion percolation is described. The
algorithm samples the critical point of a spin system without a priori
knowledge of the critical temperature and provides an efficient way to
determine the critical temperature and other observables in the critical
region. The method is illustrated for the two- and three-dimensional Ising
models. The algorithm equilibrates spin configurations much faster than the
closely related Swendsen-Wang algorithm.Comment: 13 pages RevTex and 4 Postscript figures. Submitted to Phys. Rev.
Lett. Replacement corrects problem in printing figure
Cluster Monte Carlo study of multi-component fluids of the Stillinger-Helfand and Widom-Rowlinson type
Phase transitions of fluid mixtures of the type introduced by Stillinger and
Helfand are studied using a continuum version of the invaded cluster algorithm.
Particles of the same species do not interact, but particles of different types
interact with each other via a repulsive potential. Examples of interactions
include the Gaussian molecule potential and a repulsive step potential.
Accurate values of the critical density, fugacity and magnetic exponent are
found in two and three dimensions for the two-species model. The effect of
varying the number of species and of introducing quenched impurities is also
investigated. In all the cases studied, mixtures of -species are found to
have properties similar to -state Potts models.Comment: 25 pages, 5 figure
Avoided Critical Behavior in O(n) Systems
Long-range frustrating interactions, even if their strength is infinitesimal,
can give rise to a dramatic proliferations of ground or near-ground states. As
a consequence, the ordering temperature can exhibit a discontinuous drop as a
function of the frustration. A simple model of the doped Mott insulator, where
the short-range tendency of the holes to phase separate competes with
long-range Coulomb effects, exhibits this "avoided critical" behavior. This
model may serve as a paradigm for many other systems.Comment: 4 pages, 2 figure
Invaded cluster simulations of the XY model in two and three dimensions
The invaded cluster algorithm is used to study the XY model in two and three
dimensions up to sizes 2000^2 and 120^3 respectively. A soft spin O(2) model,
in the same universality class as the 3D XY model, is also studied. The static
critical properties of the model and the dynamical properties of the algorithm
are reported. The results are K_c=0.45412(2) for the 3D XY model and
eta=0.037(2) for the 3D XY universality class. For the 2D XY model the results
are K_c=1.120(1) and eta=0.251(5). The invaded cluster algorithm does not show
any critical slowing for the magnetization or critical temperature estimator
for the 2D or 3D XY models.Comment: 30 pages, 11 figures, problem viewing figures corrected in v
Graphical representations and cluster algorithms for critical points with fields
A two-replica graphical representation and associated cluster algorithm is
described that is applicable to ferromagnetic Ising systems with arbitrary
fields. Critical points are associated with the percolation threshold of the
graphical representation. Results from numerical simulations of the Ising model
in a staggered field are presented. The dynamic exponent for the algorithm is
measured to be less than 0.5.Comment: Revtex, 12 pages with 2 figure
Algebraic Density Functionals
A systematic strategy for the calculation of density functionals (DFs)
consists in coding informations about the density and the energy into
polynomials of the degrees of freedom of wave functions. DFs and Kohn-Sham
potentials (KSPs) are then obtained by standard elimination procedures of such
degrees of freedom between the polynomials. Numerical examples illustrate the
formalism.Comment: 7 pages, 2 figures, changes to extend discussion of Kohn-Sham
potentials, and also for interacting particles. Accepted for publication in
Physics Letters
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