725 research outputs found
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
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
Revisiting the Theory of Finite Size Scaling in Disordered Systems: \nu Can Be Less Than 2/d
For phase transitions in disordered systems, an exact theorem provides a
bound on the finite size correlation length exponent: \nu_{FS}<= 2/d. It is
believed that the true critical exponent \nu of a disorder induced phase
transition satisfies the same bound. We argue that in disordered systems the
standard averaging introduces a noise, and a corresponding new diverging length
scale, characterized by \nu_{FS}=2/d. This length scale, however, is
independent of the system's own correlation length \xi. Therefore \nu can be
less than 2/d. We illustrate these ideas on two exact examples, with \nu < 2/d.
We propose a new method of disorder averaging, which achieves a remarkable
noise reduction, and thus is able to capture the true exponents.Comment: 4 pages, Latex, one figure in .eps forma
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
Monte Carlo study of the Widom-Rowlinson fluid using cluster methods
The Widom-Rowlinson model of a fluid mixture is studied using a new cluster
algorithm that is a generalization of the invaded cluster algorithm previously
applied to Potts models. Our estimate of the critical exponents for the
two-component fluid are consistent with the Ising universality class in two and
three dimensions. We also present results for the three-component fluid.Comment: 13 pages RevTex and 2 Postscript 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
Statistical Mechanics of Steiner trees
The Minimum Weight Steiner Tree (MST) is an important combinatorial
optimization problem over networks that has applications in a wide range of
fields. Here we discuss a general technique to translate the imposed global
connectivity constrain into many local ones that can be analyzed with cavity
equation techniques. This approach leads to a new optimization algorithm for
MST and allows to analyze the statistical mechanics properties of MST on random
graphs of various types
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