530 research outputs found

### Detailed Phase Transition Study at M_H <= 70 GeV in a 3-dimensional $SU(2)$--Higgs Model

We study the electroweak phase transition in an effective 3-dimensional
theory for a Higgs mass of about 70 GeV by Monte Carlo simulations. The
transition temperature and jumps of order parameters are obtained and
extrapolated to the continuum using multi-histogram techniques and finite size
analysis.Comment: Talk presented at LATTICE96(electroweak), 4 pages, 5 figure

### Multiple Histogram Method for Quantum Monte Carlo

An extension to the multiple-histogram method (sometimes referred to as the
Ferrenberg-Swendsen method) for use in quantum Monte Carlo simulations is
presented. This method is shown to work well for the 2D repulsive Hubbard
model, allowing measurements to be taken over a continuous region of
parameters. The method also reduces the error bars over the range of parameter
values due the overlapping of multiple histograms. A continuous sweep of
parameters and reduced error bars allow one to make more difficult
measurements, such as Maxwell constructions used to study phase separation.
Possibilities also exist for this method to be used for other quantum systems.Comment: 4 pages, 5 figures, RevTeX, submitted to Phys. Rev. B Rapid Com

### Depinning Transition of a Two Dimensional Vortex Lattice in a Commensurate Periodic Potential

We use Monte Carlo simulations of the 2D one component Coulomb gas on a
triangular lattice, to study the depinning transition of a 2D vortex lattice in
a commensurate periodic potential. A detailed finite size scaling analysis
indicates this transition to be first order. No significant changes in behavior
were found as vortex density was varied over a wide range.Comment: 5 pages, 8 figures. Revised discussion of correlation length exponent
using a more accurate finite size scaling analysis. New figs. 5 and 6. Old
figs. 6 and 7 now figs. 7 and

### Metastable liquid-liquid coexistence and density anomalies in a core-softened fluid

Linearly-sloped or `ramp' potentials belong to a class of core-softened
models which possess a liquid-liquid critical point (LLCP) in addition to the
usual liquid-gas critical point. Furthermore they exhibit thermodynamic
anomalies in the density and compressibility, the nature of which may be akin
to those occurring in water. Previous simulation studies of ramp potentials
have focused on just one functional form, for which the LLCP is
thermodynamically stable. In this work we construct a series of ramp
potentials, which interpolate between this previously studied form and a
ramp-based approximation to the Lennard-Jones (LJ) potential. By means of Monte
Carlo simulation, we locate the LLCP, the first order high density liquid
(HDL)-low density liquid (LDL) coexistence line, and the line of density maxima
for a selection of potentials in the series. We observe that as the LJ limit is
approached, the LLCP becomes metastable with respect to freezing into a
hexagonal close packed crystalline solid. The qualitative nature of the phase
behaviour in this regime shows a remarkable resemblance to that seen in
simulation studies of accurate water models. Specifically, the density of the
liquid phase exceeds that of the solid; the gradient of the metastable LDL-HDL
line is negative in the pressure (p)-temperature (T) plane; while the line of
density maxima in the p-T plane has a shape similar to that seen in water and
extends well into the {\em stable} liquid region of the phase diagram. As such,
our results lend weight to the `second critical point' hypothesis as an
explanation for the anomalous behaviour of water.Comment: 7 pages, 8 figure

### Site Percolation and Phase Transitions in Two Dimensions

The properties of the pure-site clusters of spin models, i.e. the clusters
which are obtained by joining nearest-neighbour spins of the same sign, are
here investigated. In the Ising model in two dimensions it is known that such
clusters undergo a percolation transition exactly at the critical point. We
show that this result is valid for a wide class of bidimensional systems
undergoing a continuous magnetization transition. We provide numerical evidence
for discrete as well as for continuous spin models, including SU(N) lattice
gauge theories. The critical percolation exponents do not coincide with the
ones of the thermal transition, but they are the same for models belonging to
the same universality class.Comment: 8 pages, 6 figures, 2 tables. Numerical part developed; figures,
references and comments adde

### Cluster Hybrid Monte Carlo Simulation Algorithms

We show that addition of Metropolis single spin-flips to the Wolff cluster
flipping Monte Carlo procedure leads to a dramatic {\bf increase} in
performance for the spin-1/2 Ising model. We also show that adding Wolff
cluster flipping to the Metropolis or heat bath algorithms in systems where
just cluster flipping is not immediately obvious (such as the spin-3/2 Ising
model) can substantially {\bf reduce} the statistical errors of the
simulations. A further advantage of these methods is that systematic errors
introduced by the use of imperfect random number generation may be largely
healed by hybridizing single spin-flips with cluster flipping.Comment: 16 pages, 10 figure

### Temperature and density extrapolations in canonical ensemble Monte Carlo simulations

We show how to use the multiple histogram method to combine canonical
ensemble Monte Carlo simulations made at different temperatures and densities.
The method can be applied to study systems of particles with arbitrary
interaction potential and to compute the thermodynamic properties over a range
of temperatures and densities. The calculation of the Helmholtz free energy
relative to some thermodynamic reference state enables us to study phase
coexistence properties. We test the method on the Lennard-Jones fluids for
which many results are available.Comment: 5 pages, 3 figure

### Universality of the Ising Model on Sphere-like Lattices

We study the 2D Ising model on three different types of lattices that are
topologically equivalent to spheres. The geometrical shapes are reminiscent of
the surface of a pillow, a 3D cube and a sphere, respectively. Systems of
volumes ranging up to O($10^5$) sites are simulated and finite size scaling is
analyzed. The partition function zeros and the values of various cumulants at
their respective peak positions are determined and they agree with the scaling
behavior expected from universality with the Onsager solution on the torus
($\nu=1$). For the pseudocritical values of the coupling we find significant
anomalies indicating a shift exponent $\neq 1$ for sphere-like lattice
topology.Comment: 24 pages, LaTeX, 8 figure

### Non-perturbative determination of anisotropy coefficients in lattice gauge theories

We propose a new non-perturbative method to compute derivatives of gauge
coupling constants with respect to anisotropic lattice spacings (anisotropy
coefficients), which are required in an evaluation of thermodynamic quantities
from numerical simulations on the lattice. Our method is based on a precise
measurement of the finite temperature deconfining transition curve in the
lattice coupling parameter space extended to anisotropic lattices by applying
the spectral density method. We test the method for the cases of SU(2) and
SU(3) gauge theories at the deconfining transition point on lattices with the
lattice size in the time direction $N_t=4$ -- 6. In both cases, there is a
clear discrepancy between our results and perturbative values. A longstanding
problem, when one uses the perturbative anisotropy coefficients, is a
non-vanishing pressure gap at the deconfining transition point in the SU(3)
gauge theory. Using our non-perturbative anisotropy coefficients, we find that
this problem is completely resolved: we obtain $\Delta p/T^4 = 0.001(15)$ and
$-0.003(17)$ on $N_t=4$ and 6 lattices, respectively.Comment: 24pages,7figures,5table

### Magnetic Phase Diagram of the Ferromagnetically Stacked Triangular XY Antiferromagnet: A Finite-Size Scaling Study

Histogram Monte-Carlo simulation results are presented for the magnetic-field
-- temperature phase diagram of the XY model on a stacked triangular lattice
with antiferromagnetic intraplane and ferromagnetic interplane interactions.
Finite-size scaling results at the various transition boundaries are consistent
with expectations based on symmetry arguments. Although a molecular-field
treatment of the Hamiltonian fails to reproduce the correct structure for the
phase diagram, it is demonstrated that a phenomenological Landau-type
free-energy model contains all the esstential features. These results serve to
complement and extend our earlier work [Phys. Rev. B {\bf 48}, 3840 (1993)].Comment: 5 pages (RevTex 3.0), 6 figures available upon request, CRPS 93-

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