209 research outputs found
Graphical Representations for Ising Systems in External Fields
A graphical representation based on duplication is developed that is suitable
for the study of Ising systems in external fields. Two independent replicas of
the Ising system in the same field are treated as a single four-state
(Ashkin-Teller) model. Bonds in the graphical representation connect the
Ashkin-Teller spins. For ferromagnetic systems it is proved that ordering is
characterized by percolation in this representation. The representation leads
immediately to cluster algorithms; some applications along these lines are
discussed.Comment: 13 pages amste
Percolation in the Sherrington-Kirkpatrick Spin Glass
We present extended versions and give detailed proofs of results concerning
percolation (using various sets of two-replica bond occupation variables) in
Sherrington-Kirkpatrick spin glasses (with zero external field) that were first
given in an earlier paper by the same authors. We also explain how
ultrametricity is manifested by the densities of large percolating clusters.
Our main theorems concern the connection between these densities and the usual
spin overlap distribution. Their corollaries are that the ordered spin glass
phase is characterized by a unique percolating cluster of maximal density
(normally coexisting with a second cluster of nonzero but lower density). The
proofs involve comparison inequalities between SK multireplica bond occupation
variables and the independent variables of standard Erdos-Renyi random graphs.Comment: 18 page
Nature vs. Nurture: Predictability in Low-Temperature Ising Dynamics
Consider a dynamical many-body system with a random initial state
subsequently evolving through stochastic dynamics. What is the relative
importance of the initial state ("nature") vs. the realization of the
stochastic dynamics ("nurture") in predicting the final state? We examined this
question for the two-dimensional Ising ferromagnet following an initial deep
quench from to . We performed Monte Carlo studies on the
overlap between "identical twins" raised in independent dynamical environments,
up to size . Our results suggest an overlap decaying with time as
with ; the same exponent holds for a
quench to low but nonzero temperature. This "heritability exponent" may equal
the persistence exponent for the 2D Ising ferromagnet, but the two differ more
generally.Comment: 5 pages, 3 figures; new version includes results for nonzero
temperatur
Dynamic and static properties of the invaded cluster algorithm
Simulations of the two-dimensional Ising and 3-state Potts models at their
critical points are performed using the invaded cluster (IC) algorithm. It is
argued that observables measured on a sub-lattice of size l should exhibit a
crossover to Swendsen-Wang (SW) behavior for l sufficiently less than the
lattice size L, and a scaling form is proposed to describe the crossover
phenomenon. It is found that the energy autocorrelation time tau(l,L) for an
l*l sub-lattice attains a maximum in the crossover region, and a dynamic
exponent z for the IC algorithm is defined according to tau_max ~ L^z.
Simulation results for the 3-state model yield z=.346(.002) which is smaller
than values of the dynamic exponent found for the SW and Wolff algorithms and
also less than the Li-Sokal bound. The results are less conclusive for the
Ising model, but it appears that z<.21 and possibly that tau_max ~ log L so
that z=0 -- similar to previous results for the SW and Wolff algorithms.Comment: 21 pages with 12 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
The Computational Complexity of Generating Random Fractals
In this paper we examine a number of models that generate random fractals.
The models are studied using the tools of computational complexity theory from
the perspective of parallel computation. Diffusion limited aggregation and
several widely used algorithms for equilibrating the Ising model are shown to
be highly sequential; it is unlikely they can be simulated efficiently in
parallel. This is in contrast to Mandelbrot percolation that can be simulated
in constant parallel time. Our research helps shed light on the intrinsic
complexity of these models relative to each other and to different growth
processes that have been recently studied using complexity theory. In addition,
the results may serve as a guide to simulation physics.Comment: 28 pages, LATEX, 8 Postscript figures available from
[email protected]
Experimental observations of dynamic critical phenomena in a lipid membrane
Near a critical point, the time scale of thermally-induced fluctuations
diverges in a manner determined by the dynamic universality class. Experiments
have verified predicted 3D dynamic critical exponents in many systems, but
similar experiments in 2D have been lacking for the case of conserved order
parameter. Here we analyze time-dependent correlation functions of a quasi-2D
lipid bilayer in water to show that its critical dynamics agree with a recently
predicted universality class. In particular, the effective dynamic exponent
crosses over from to as the correlation
length of fluctuations exceeds a hydrodynamic length set by the membrane and
bulk viscosities.Comment: 5 pages, 3 figures and 2 additional pages of supplemen
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