4,471 research outputs found

### 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

### 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.

### 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

### 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

### Equilibrium fluid-solid coexistence of hard spheres

We present a tethered Monte Carlo simulation of the crystallization of hard
spheres. Our method boosts the traditional umbrella sampling to the point of
making practical the study of constrained Gibb's free energies depending on
several crystalline order-parameters. We obtain high-accuracy estimates of the
fluid-crystal coexistence pressure for up to 2916 particles (enough to
accommodate fluid-solid interfaces). We are able to extrapolate to infinite
volume the coexistence pressure (p_{co}=11.5727(10) k_B T/\sigma^3) and the
interfacial free energy (\gamma_{100}=0.636(11) k_B T/\sigma^2).Comment: 6 pages, 4 pdf figures. Version to be published in PRL. Appendices
contain Supplemental Materia

### Completeness of the classical 2D Ising model and universal quantum computation

We prove that the 2D Ising model is complete in the sense that the partition
function of any classical q-state spin model (on an arbitrary graph) can be
expressed as a special instance of the partition function of a 2D Ising model
with complex inhomogeneous couplings and external fields. In the case where the
original model is an Ising or Potts-type model, we find that the corresponding
2D square lattice requires only polynomially more spins w.r.t the original one,
and we give a constructive method to map such models to the 2D Ising model. For
more general models the overhead in system size may be exponential. The results
are established by connecting classical spin models with measurement-based
quantum computation and invoking the universality of the 2D cluster states.Comment: 4 pages, 1 figure. Minor change

### Critical speeding-up in a local dynamics for the random-cluster model

We study the dynamic critical behavior of the local bond-update (Sweeny)
dynamics for the Fortuin-Kasteleyn random-cluster model in dimensions d=2,3, by
Monte Carlo simulation. We show that, for a suitable range of q values, the
global observable S_2 exhibits "critical speeding-up": it decorrelates well on
time scales much less than one sweep, so that the integrated autocorrelation
time tends to zero as the critical point is approached. We also show that the
dynamic critical exponent z_{exp} is very close (possibly equal) to the
rigorous lower bound \alpha/\nu, and quite possibly smaller than the
corresponding exponent for the Chayes-Machta-Swendsen-Wang cluster dynamics.Comment: LaTex2e/revtex4, 4 pages, includes 5 figure

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