400 research outputs found
Phase Transitions in the Multicomponent Widom-Rowlinson Model and in Hard Cubes on the BCC--Lattice
We use Monte Carlo techniques and analytical methods to study the phase
diagram of the M--component Widom-Rowlinson model on the bcc-lattice: there are
M species all with the same fugacity z and a nearest neighbor hard core
exclusion between unlike particles. Simulations show that for M greater or
equal 3 there is a ``crystal phase'' for z lying between z_c(M) and z_d(M)
while for z > z_d(M) there are M demixed phases each consisting mostly of one
species. For M=2 there is a direct second order transition from the gas phase
to the demixed phase while for M greater or equal 3 the transition at z_d(M)
appears to be first order putting it in the Potts model universality class. For
M large, Pirogov-Sinai theory gives z_d(M) ~ M-2+2/(3M^2) + ... . In the
crystal phase the particles preferentially occupy one of the sublattices,
independent of species, i.e. spatial symmetry but not particle symmetry is
broken. For M to infinity this transition approaches that of the one component
hard cube gas with fugacity y = zM. We find by direct simulations of such a
system a transition at y_c ~ 0.71 which is consistent with the simulation
z_c(M) for large M. This transition appears to be always of the Ising type.Comment: 11 pages, 4 postscript figures (added in replacement), Physica A (in
press
Confinement Effects in Antiferromagnets
Phase equilibrium in confined Ising antiferromagnets was studied as a
function of the coupling (v) and a magnetic field (h) at the surfaces, in the
presence of an external field H. The ground state properties were calculated
exactly for symmetric boundary conditions and nearest-neighbor interactions,
and a full zero-temperature phase diagram in the plane v-h was obtained for
films with symmetry-preserving surface orientations. The ground-state analysis
was extended to the H-T plane using a cluster-variation free energy. The study
of the finite-T properties (as a function of v and h) reveals the close
interdependence between the surface and finite-size effects and, together with
the ground-state phase diagram, provides an integral picture of the confinement
in anisotropic antiferromagnets with surfaces that preserve the symmetry of the
order parameter.Comment: 10 pages, 8 figures, Accepted in Phys. Rev.
Ordering and Demixing Transitions in Multicomponent Widom-Rowlinson Models
We use Monte Carlo techniques and analytical methods to study the phase
diagram of multicomponent Widom-Rowlinson models on a square lattice: there are
M species all with the same fugacity z and a nearest neighbor hard core
exclusion between unlike particles. Simulations show that for M between two and
six there is a direct transition from the gas phase at z < z_d (M) to a demixed
phase consisting mostly of one species at z > z_d (M) while for M \geq 7 there
is an intermediate ``crystal phase'' for z lying between z_c(M) and z_d(M). In
this phase, which is driven by entropy, particles, independent of species,
preferentially occupy one of the sublattices, i.e. spatial symmetry but not
particle symmetry is broken. The transition at z_d(M) appears to be first order
for M \geq 5 putting it in the Potts model universality class. For large M the
transition between the crystalline and demixed phase at z_d(M) can be proven to
be first order with z_d(M) \sim M-2 + 1/M + ..., while z_c(M) is argued to
behave as \mu_{cr}/M, with \mu_{cr} the value of the fugacity at which the one
component hard square lattice gas has a transition, and to be always of the
Ising type. Explicit calculations for the Bethe lattice with the coordination
number q=4 give results similar to those for the square lattice except that the
transition at z_d(M) becomes first order at M>2. This happens for all q,
consistent with the model being in the Potts universality class.Comment: 26 pages, 15 postscript figure
Reexamination of the long-range Potts model: a multicanonical approach
We investigate the critical behavior of the one-dimensional q-state Potts
model with long-range (LR) interaction , using a multicanonical
algorithm. The recursion scheme initially proposed by Berg is improved so as to
make it suitable for a large class of LR models with unequally spaced energy
levels. The choice of an efficient predictor and a reliable convergence
criterion is discussed. We obtain transition temperatures in the first-order
regime which are in far better agreement with mean-field predictions than in
previous Monte Carlo studies. By relying on the location of spinodal points and
resorting to scaling arguments, we determine the threshold value
separating the first- and second-order regimes to two-digit precision within
the range . We offer convincing numerical evidence supporting
$\sigma_c(q)Comment: 18 pages, 18 figure
Stability of mode-locked kinks in the ac driven and damped sine-Gordon lattice
Kink dynamics in the underdamped and strongly discrete sine-Gordon lattice
that is driven by the oscillating force is studied. The investigation is
focused mostly on the properties of the mode-locked states in the {\it
overband} case, when the driving frequency lies above the linear band. With the
help of Floquet theory it is demonstrated that the destabilizing of the
mode-locked state happens either through the Hopf bifurcation or through the
tangential bifurcation. It is also observed that in the overband case the
standing mode-locked kink state maintains its stability for the bias amplitudes
that are by the order of magnitude larger than the amplitudes in the
low-frequency case.Comment: To appear in Springer Series on Wave Phenomena, special volume
devoted to the LENCOS'12 conference; 6 figure
Simulation of Potts models with real q and no critical slowing down
A Monte Carlo algorithm is proposed to simulate ferromagnetic q-state Potts
model for any real q>0. A single update is a random sequence of disordering and
deterministic moves, one for each link of the lattice. A disordering move
attributes a random value to the link, regardless of the state of the system,
while in a deterministic move this value is a state function. The relative
frequency of these moves depends on the two parameters q and beta. The
algorithm is not affected by critical slowing down and the dynamical critical
exponent z is exactly vanishing. We simulate in this way a 3D Potts model in
the range 2<q<3 for estimating the critical value q_c where the thermal
transition changes from second-order to first-order, and find q_c=2.620(5).Comment: 5 pages, 3 figures slightly extended version, to appear in Phys. Rev.
Generating a checking sequence with a minimum number of reset transitions
Given a finite state machine M, a checking sequence is an input sequence that is guaranteed to lead to a failure if the implementation under test is faulty and has no more states than M. There has been much interest in the automated generation of a short checking sequence from a finite state machine. However, such sequences can contain reset transitions whose use can adversely affect both the cost of applying the checking sequence and the effectiveness of the checking sequence. Thus, we sometimes want a checking sequence with a minimum number of reset transitions rather than a shortest checking sequence. This paper describes a new algorithm for generating a checking sequence, based on a distinguishing sequence, that minimises the number of reset transitions used.This work was supported in part by Leverhulme Trust grant number F/00275/D, Testing State Based Systems, Natural Sciences and Engineering Research Council (NSERC) of Canada grant number RGPIN 976, and Engineering and Physical Sciences Research Council grant number GR/R43150, Formal Methods and Testing (FORTEST)
The Harris-Luck criterion for random lattices
The Harris-Luck criterion judges the relevance of (potentially) spatially
correlated, quenched disorder induced by, e.g., random bonds, randomly diluted
sites or a quasi-periodicity of the lattice, for altering the critical behavior
of a coupled matter system. We investigate the applicability of this type of
criterion to the case of spin variables coupled to random lattices. Their
aptitude to alter critical behavior depends on the degree of spatial
correlations present, which is quantified by a wandering exponent. We consider
the cases of Poissonian random graphs resulting from the Voronoi-Delaunay
construction and of planar, ``fat'' Feynman diagrams and precisely
determine their wandering exponents. The resulting predictions are compared to
various exact and numerical results for the Potts model coupled to these
quenched ensembles of random graphs.Comment: 13 pages, 9 figures, 2 tables, REVTeX 4. Version as published, one
figure added for clarification, minor re-wordings and typo cleanu
Calculation of ground states of four-dimensional +or- J Ising spin glasses
Ground states of four-dimensional (d=4) EA Ising spin glasses are calculated
for sizes up to 7x7x7x7 using a combination of a genetic algorithm and
cluster-exact approximation. The ground-state energy of the infinite system is
extrapolated as e_0=-2.095(1). The ground-state stiffness (or domain wall)
energy D is calculated. A D~L^{\Theta} behavior with \Theta=0.65(4) is found
which confirms that the d=4 model has an equilibrium spin-glass-paramagnet
transition for non-zero T_c.Comment: 5 pages, 3 figures, 31 references, revtex; update of reference
Edge effects in a frustrated Josephson junction array with modulated couplings
A square array of Josephson junctions with modulated strength in a magnetic
field with half a flux quantum per plaquette is studied by analytic arguments
and dynamical simulations. The modulation is such that alternate columns of
junctions are of different strength to the rest. Previous work has shown that
this system undergoes an XY followed by an Ising-like vortex lattice
disordering transition at a lower temperature. We argue that resistance
measurements are a possible probe of the vortex lattice disordering transition
as the linear resistance with
at intermediate temperatures due to dissipation at the array
edges for a particular geometry and vanishes for other geometries. Extensive
dynamical simulations are performed which support the qualitative physical
arguments.Comment: 8 pages with figs, RevTeX, to appear in Phys. Rev.
- …