426 research outputs found
A Geometrical Interpretation of Hyperscaling Breaking in the Ising Model
In random percolation one finds that the mean field regime above the upper
critical dimension can simply be explained through the coexistence of infinite
percolating clusters at the critical point. Because of the mapping between
percolation and critical behaviour in the Ising model, one might check whether
the breakdown of hyperscaling in the Ising model can also be intepreted as due
to an infinite multiplicity of percolating Fortuin-Kasteleyn clusters at the
critical temperature T_c. Preliminary results suggest that the scenario is much
more involved than expected due to the fact that the percolation variables
behave differently on the two sides of T_c.Comment: Lattice2002(spin
SLE in the three-state Potts model - a numerical study
The scaling limit of the spin cluster boundaries of the Ising model with
domain wall boundary conditions is SLE with kappa=3. We hypothesise that the
three-state Potts model with appropriate boundary conditions has spin cluster
boundaries which are also SLE in the scaling limit, but with kappa=10/3. To
test this, we generate samples using the Wolff algorithm and test them against
predictions of SLE: we examine the statistics of the Loewner driving function,
estimate the fractal dimension and test against Schramm's formula. The results
are in support of our hypothesis.Comment: 32 pages, 41 figure
Exact Potts Model Partition Functions for Strips of the Honeycomb Lattice
We present exact calculations of the Potts model partition function
for arbitrary and temperature-like variable on -vertex
strip graphs of the honeycomb lattice for a variety of transverse widths
equal to vertices and for arbitrarily great length, with free
longitudinal boundary conditions and free and periodic transverse boundary
conditions. These partition functions have the form
, where
denotes the number of repeated subgraphs in the longitudinal direction. We give
general formulas for for arbitrary . We also present plots of
zeros of the partition function in the plane for various values of and
in the plane for various values of . Explicit results for partition
functions are given in the text for (free) and (cylindrical),
and plots of partition function zeros are given for up to 5 (free) and
(cylindrical). Plots of the internal energy and specific heat per site
for infinite-length strips are also presented.Comment: 39 pages, 34 eps figures, 3 sty file
Center clusters in the Yang-Mills vacuum
Properties of local Polyakov loops for SU(2) and SU(3) lattice gauge theory
at finite temperature are analyzed. We show that spatial clusters can be
identified where the local Polyakov loops have values close to the same center
element. For a suitable definition of these clusters the deconfinement
transition can be characterized by the onset of percolation in one of the
center sectors. The analysis is repeated for different resolution scales of the
lattice and we argue that the center clusters have a continuum limit.Comment: Table added. Final version to appear in JHE
Percolation on the average and spontaneous magnetization for q-states Potts model on graph
We prove that the q-states Potts model on graph is spontaneously magnetized
at finite temperature if and only if the graph presents percolation on the
average. Percolation on the average is a combinatorial problem defined by
averaging over all the sites of the graph the probability of belonging to a
cluster of a given size. In the paper we obtain an inequality between this
average probability and the average magnetization, which is a typical extensive
function describing the thermodynamic behaviour of the model
On the non-ergodicity of the Swendsen-Wang-Kotecky algorithm on the kagome lattice
We study the properties of the Wang-Swendsen-Kotecky cluster Monte Carlo
algorithm for simulating the 3-state kagome-lattice Potts antiferromagnet at
zero temperature. We prove that this algorithm is not ergodic for symmetric
subsets of the kagome lattice with fully periodic boundary conditions: given an
initial configuration, not all configurations are accessible via Monte Carlo
steps. The same conclusion holds for single-site dynamics.Comment: Latex2e. 22 pages. Contains 11 figures using pstricks package. Uses
iopart.sty. Final version accepted in journa
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
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