227 research outputs found
Exact sampling from non-attractive distributions using summary states
Propp and Wilson's method of coupling from the past allows one to efficiently
generate exact samples from attractive statistical distributions (e.g., the
ferromagnetic Ising model). This method may be generalized to non-attractive
distributions by the use of summary states, as first described by Huber. Using
this method, we present exact samples from a frustrated antiferromagnetic
triangular Ising model and the antiferromagnetic q=3 Potts model. We discuss
the advantages and limitations of the method of summary states for practical
sampling, paying particular attention to the slowing down of the algorithm at
low temperature. In particular, we show that such a slowing down can occur in
the absence of a physical phase transition.Comment: 5 pages, 6 EPS figures, REVTeX; additional information at
http://wol.ra.phy.cam.ac.uk/mackay/exac
The Thermodynamics of Quarks and Gluons
This is an introduction to the study of strongly interacting matter. We
survey its different possible states and discuss the transition from hadronic
matter to a plasma of deconfined quarks and gluons. Following this, we
summarize the results provided by lattice QCD finite temperature and density,
and then investigate the nature of the deconfinement transition. Finally we
give a schematic overview of possible ways to study the properties of the
quark-gluon plasma.Comment: 19 pages, 21 figures; lecture given at the QGP Winter School,
Jaipur/India, Feb.1-3, 2008; to appear in Springer Lecture Notes in Physic
Dynamic Critical Behavior of the Chayes-Machta Algorithm for the Random-Cluster Model. I. Two Dimensions
We study, via Monte Carlo simulation, the dynamic critical behavior of the
Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which
generalizes the Swendsen-Wang dynamics for the q-state Potts ferromagnet to
non-integer q \ge 1. We consider spatial dimension d=2 and 1.25 \le q \le 4 in
steps of 0.25, on lattices up to 1024^2, and obtain estimates for the dynamic
critical exponent z_{CM}. We present evidence that when 1 \le q \lesssim 1.95
the Ossola-Sokal conjecture z_{CM} \ge \beta/\nu is violated, though we also
present plausible fits compatible with this conjecture. We show that the
Li-Sokal bound z_{CM} \ge \alpha/\nu is close to being sharp over the entire
range 1 \le q \le 4, but is probably non-sharp by a power. As a byproduct of
our work, we also obtain evidence concerning the corrections to scaling in
static observables.Comment: LaTeX2e, 75 pages including 26 Postscript figure
The O(n) model on the annulus
We use Coulomb gas methods to propose an explicit form for the scaling limit
of the partition function of the critical O(n) model on an annulus, with free
boundary conditions, as a function of its modulus. This correctly takes into
account the magnetic charge asymmetry and the decoupling of the null states. It
agrees with an earlier conjecture based on Bethe ansatz and quantum group
symmetry, and with all known results for special values of n. It gives new
formulae for percolation (the probability that a cluster connects the two
opposite boundaries) and for self-avoiding loops (the partition function for a
single loop wrapping non-trivially around the annulus.) The limit n->0 also
gives explicit examples of partition functions in logarithmic conformal field
theory.Comment: 20 pp. v.2: important references added to earlier work, minor typos
correcte
Dynamic Critical Behavior of the Swendsen-Wang Algorithm: The Two-Dimensional 3-State Potts Model Revisited
We have performed a high-precision Monte Carlo study of the dynamic critical
behavior of the Swendsen-Wang algorithm for the two-dimensional 3-state Potts
model. We find that the Li-Sokal bound ()
is almost but not quite sharp. The ratio seems to diverge
either as a small power () or as a logarithm.Comment: 35 pages including 3 figures. Self-unpacking file containing the
LaTeX file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and
eqsection.sty) and the 3 Postscript figures. Revised version fixes a
normalization error in \xi (with many thanks to Wolfhard Janke for finding
the error!). To be published in J. Stat. Phys. 87, no. 1/2 (April 1997
Combination of improved multibondic method and the Wang-Landau method
We propose a method for Monte Carlo simulation of statistical physical models
with discretized energy. The method is based on several ideas including the
cluster algorithm, the multicanonical Monte Carlo method and its acceleration
proposed recently by Wang and Landau. As in the multibondic ensemble method
proposed by Janke and Kappler, the present algorithm performs a random walk in
the space of the bond population to yield the state density as a function of
the bond number. A test on the Ising model shows that the number of Monte Carlo
sweeps required of the present method for obtaining the density of state with a
given accuracy is proportional to the system size, whereas it is proportional
to the system size squared for other conventional methods. In addition, the new
method shows a better performance than the original Wang-Landau method in
measurement of physical quantities.Comment: 12 pages, 3 figure
Crossover from Isotropic to Directed Percolation
Directed percolation is one of the generic universality classes for dynamic
processes. We study the crossover from isotropic to directed percolation by
representing the combined problem as a random cluster model, with a parameter
controlling the spontaneous birth of new forest fires. We obtain the exact
crossover exponent at using Coulomb gas methods in 2D.
Isotropic percolation is stable, as is confirmed by numerical finite-size
scaling results. For , the stability seems to change. An intuitive
argument, however, suggests that directed percolation at is unstable and
that the scaling properties of forest fires at intermediate values of are
in the same universality class as isotropic percolation, not only in 2D, but in
all dimensions.Comment: 4 pages, REVTeX, 4 epsf-emedded postscript figure
Cluster Percolation in O(n) Spin Models
The spontaneous symmetry breaking in the Ising model can be equivalently
described in terms of percolation of Wolff clusters. In O(n) spin models
similar clusters can be built in a general way, and they are currently used to
update these systems in Monte Carlo simulations. We show that for 3-dimensional
O(2), O(3) and O(4) such clusters are indeed the physical `islands' of the
systems, i.e., they percolate at the physical threshold and the percolation
exponents are in the universality class of the corresponding model. For O(2)
and O(3) the result is proven analytically, for O(4) we derived it by numerical
simulations.Comment: 11 pages, 8 figures, 2 tables, minor modification
A Swendsen-Wang update algorithm for the Symanzik improved sigma model
We study a generalization of Swendsen-Wang algorithm suited for Potts models
with next-next-neighborhood interactions. Using the embedding technique
proposed by Wolff we test it on the Symanzik improved bidimensional non-linear
model. For some long range observables we find a little slowing down
exponent () that we interpret as an effect of the partial
frustration of the induced spin model.Comment: Self extracting archive fil
Broad histogram relation for the bond number and its applications
We discuss Monte Carlo methods based on the cluster (graph) representation
for spin models. We derive a rigorous broad histogram relation (BHR) for the
bond number; a counterpart for the energy was derived by Oliveira previously. A
Monte Carlo dynamics based on the number of potential moves for the bond number
is proposed. We show the efficiency of the BHR for the bond number in
calculating the density of states and other physical quantities.Comment: 7 pages, 7 figure
- …