8,509 research outputs found
Grassmann Integral Representation for Spanning Hyperforests
Given a hypergraph G, we introduce a Grassmann algebra over the vertex set,
and show that a class of Grassmann integrals permits an expansion in terms of
spanning hyperforests. Special cases provide the generating functions for
rooted and unrooted spanning (hyper)forests and spanning (hyper)trees. All
these results are generalizations of Kirchhoff's matrix-tree theorem.
Furthermore, we show that the class of integrals describing unrooted spanning
(hyper)forests is induced by a theory with an underlying OSP(1|2)
supersymmetry.Comment: 50 pages, it uses some latex macros. Accepted for publication on J.
Phys.
Ferromagnetic phase transition for the spanning-forest model (q \to 0 limit of the Potts model) in three or more dimensions
We present Monte Carlo simulations of the spanning-forest model (q \to 0
limit of the ferromagnetic Potts model) in spatial dimensions d=3,4,5. We show
that, in contrast to the two-dimensional case, the model has a "ferromagnetic"
second-order phase transition at a finite positive value w_c. We present
numerical estimates of w_c and of the thermal and magnetic critical exponents.
We conjecture that the upper critical dimension is 6.Comment: LaTex2e, 4 pages; includes 6 Postscript figures; Version 2 has
expanded title as published in PR
Dynamic critical behavior of the Chayes-Machta-Swendsen-Wang algorithm
We study 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 model to noninteger q, in two and three spatial
dimensions, by Monte Carlo simulation. We show that the Li-Sokal bound z \ge
\alpha/\nu is close to but probably not sharp in d=2, and is far from sharp in
d=3, for all q. The conjecture z \ge \beta/\nu is false (for some values of q)
in both d=2 and d=3.Comment: Revtex4, 4 pages including 4 figure
Dynamic relaxation of a liquid cavity under amorphous boundary conditions
The growth of cooperatively rearranging regions was invoked long ago by Adam
and Gibbs to explain the slowing down of glass-forming liquids. The lack of
knowledge about the nature of the growing order, though, complicates the
definition of an appropriate correlation function. One option is the
point-to-set correlation function, which measures the spatial span of the
influence of amorphous boundary conditions on a confined system. By using a
swap Monte Carlo algorithm we measure the equilibration time of a liquid
droplet bounded by amorphous boundary conditions in a model glass-former at low
temperature, and we show that the cavity relaxation time increases with the
size of the droplet, saturating to the bulk value when the droplet outgrows the
point-to-set correlation length. This fact supports the idea that the
point-to-set correlation length is the natural size of the cooperatively
rearranging regions. On the other hand, the cavity relaxation time computed by
a standard, nonswap dynamics, has the opposite behavior, showing a very steep
increase when the cavity size is decreased. We try to reconcile this difference
by discussing the possible hybridization between MCT and activated processes,
and by introducing a new kind of amorphous boundary conditions, inspired by the
concept of frozen external state as an alternative to the commonly used frozen
external configuration.Comment: Completely rewritten version. After the first submission it was
realized that swap and nonswap dynamics results are qualitatively different.
This version reports the results of both dynamics and discusses the different
behaviors. 17 pages, 18 figure
Cluster simulations of loop models on two-dimensional lattices
We develop cluster algorithms for a broad class of loop models on
two-dimensional lattices, including several standard O(n) loop models at n \ge
1. We show that our algorithm has little or no critical slowing-down when 1 \le
n \le 2. We use this algorithm to investigate the honeycomb-lattice O(n) loop
model, for which we determine several new critical exponents, and a
square-lattice O(n) loop model, for which we obtain new information on the
phase diagram.Comment: LaTex2e, 4 pages; includes 1 table and 2 figures. Totally rewritten
in version 2, with new theory and new data. Version 3 as published in PR
New X-ray Detections of WNL Stars
Previous studies have demonstrated that putatively single nitrogen-type
Wolf-Rayet stars (WN stars) without known companions are X-ray sources.
However, almost all WN star X-ray detections so far have been of earlier WN2 -
WN6 spectral subtypes. Later WN7 - WN9 subtypes (also known as WNL stars) have
proved more difficult to detect, an important exception being WR 79a (WN9ha).
We present here new X-ray detections of the WNL stars WR 16 (WN8h) and WR 78
(WN7h). These new results, when combined with previous detections, demonstrate
that X-ray emission is present in WN stars across the full range of spectral
types, including later WNL stars. The two WN8 stars observed to date (WR 16 and
WR 40) show unusually low X-ray luminosities (Lx) compared to other WN stars,
and it is noteworthy that they also have the lowest terminal wind speeds
(v_infty). Existing X-ray detections of about a dozen WN stars reveal a trend
of increasing Lx with wind luminosity Lwind = (1/2) M_dot v_infty^2, suggesting
that wind kinetic energy may play a key role in establishing X-ray luminosity
levels in WN stars.Comment: 20 pages, 5 figure
Approximating the partition function of the ferromagnetic Potts model
We provide evidence that it is computationally difficult to approximate the
partition function of the ferromagnetic q-state Potts model when q>2.
Specifically we show that the partition function is hard for the complexity
class #RHPi_1 under approximation-preserving reducibility. Thus, it is as hard
to approximate the partition function as it is to find approximate solutions to
a wide range of counting problems, including that of determining the number of
independent sets in a bipartite graph. Our proof exploits the first order phase
transition of the "random cluster" model, which is a probability distribution
on graphs that is closely related to the q-state Potts model.Comment: Minor correction
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