262 research outputs found
Discretization Errors and Rotational Symmetry: The Laplacian Operator on Non-Hypercubical Lattices
Discretizations of the Laplacian operator on non-hypercubical lattices are
discussed in a systematic approach. It is shown that order errors always
exist for discretizations involving only nearest neighbors. Among all lattices
with the same density of lattice sites, the hypercubical lattices always have
errors smaller than other lattices with the same number of spacetime
dimensions. On the other hand, the four dimensional checkerboard lattice (also
known as the Celmaster lattice) is the only lattice which is isotropic at order
. Explicit forms of the discretized Laplacian operators on root lattices
are presented, and different ways of eliminating order errors are
discussed.Comment: 30 pages in REVTe
Temporal Correlations and Persistence in the Kinetic Ising Model: the Role of Temperature
We study the statistical properties of the sum , that is the difference of time spent positive or negative by the
spin , located at a given site of a -dimensional Ising model
evolving under Glauber dynamics from a random initial configuration. We
investigate the distribution of and the first-passage statistics
(persistence) of this quantity. We discuss successively the three regimes of
high temperature (), criticality (), and low temperature
(). We discuss in particular the question of the temperature
dependence of the persistence exponent , as well as that of the
spectrum of exponents , in the low temperature phase. The
probability that the temporal mean was always larger than the
equilibrium magnetization is found to decay as . This
yields a numerical determination of the persistence exponent in the
whole low temperature phase, in two dimensions, and above the roughening
transition, in the low-temperature phase of the three-dimensional Ising model.Comment: 21 pages, 11 PostScript figures included (1 color figure
Simplicial gauge theory on spacetime
We define a discrete gauge-invariant Yang-Mills-Higgs action on spacetime
simplicial meshes. The formulation is a generalization of classical lattice
gauge theory, and we prove consistency of the action in the sense of
approximation theory. In addition, we perform numerical tests of convergence
towards exact continuum results for several choices of gauge fields in pure
gauge theory.Comment: 18 pages, 2 figure
Z_N Gauge Theories on a Lattice and Quantum Memory
In the present paper we shall study (2+1) dimensional Z_N gauge theories on a
lattice. It is shown that the gauge theories have two phases, one is a Higgs
phase and the other is a confinement phase. We investigate low-energy
excitation modes in the Higgs phase and clarify relationship between the Z_N
gauge theories and Kitaev's model for quantum memory and quantum computations.
Then we study effects of random gauge couplings(RGC) which are identified with
noise and errors in quantum computations by Kitaev's model. By using a duality
transformation, it is shown that time-independent RGC give no significant
effects on the phase structure and the stability of quantum memory and
computations. Then by using the replica methods, we study Z_N gauge theories
with time-dependent RGC and show that nontrivial phase transitions occur by the
RGC.Comment: 20 pages, 5 figure
Matrix string interactions
String configurations have been identified in compactified Matrix theory at
vanishing string coupling. We show how the interactions of these strings are
determined by the Yang-Mills gauge field on the worldsheet. At finite string
coupling, this suggests the underlying dynamics is not well-approximated as a
theory of strings. This may explain why string perturbation theory diverges
badly, while Matrix string perturbation theory presumably has a perturbative
expansion with properties similar to the strong coupling expansion of 2d
Yang-Mills theory.Comment: 2 pages, latex, minor clarifying changes of wordin
The Kovacs effect in model glasses
We discuss the `memory effect' discovered in the 60's by Kovacs in
temperature shift experiments on glassy polymers, where the volume (or energy)
displays a non monotonous time behaviour. This effect is generic and is
observed on a variety of different glassy systems (including granular
materials). The aim of this paper is to discuss whether some microscopic
information can be extracted from a quantitative analysis of the `Kovacs hump'.
We study analytically two families of theoretical models: domain growth and
traps, for which detailed predictions of the shape of the hump can be obtained.
Qualitatively, the Kovacs effect reflects the heterogeneity of the system: its
description requires to deal not only with averages but with a full probability
distribution (of domain sizes or of relaxation times). We end by some
suggestions for a quantitative analysis of experimental results.Comment: 17 pages, 6 figures; revised versio
Coarsening and persistence in a class of stochastic processes interpolating between the Ising and voter models
We study the dynamics of a class of two dimensional stochastic processes,
depending on two parameters, which may be interpreted as two different
temperatures, respectively associated to interfacial and to bulk noise. Special
lines in the plane of parameters correspond to the Ising model, voter model and
majority vote model. The dynamics of this class of models may be described
formally in terms of reaction diffusion processes for a set of coalescing,
annihilating, and branching random walkers. We use the freedom allowed by the
space of parameters to measure, by numerical simulations, the persistence
probability of a generic model in the low temperature phase, where the system
coarsens. This probability is found to decay at large times as a power law with
a seemingly constant exponent . We also discuss the
connection between persistence and the nature of the interfaces between
domains.Comment: Late
Master Wilson loop operators in large-N lattice QCD
An explicit solution is found for the most general independent correlation
functions in lattice QCD with Wilson action. The large- limit of these
correlations may be used to reconstruct the eigenvalue distributions of Wilson
loop operators for arbitrary loops. Properties of these spectral densities are
discussed in the region .Comment: 7 pages, Revtex, 2 figures (ps files appended at the end of the
Revtex file
A simple stochastic model for the dynamics of condensation
We consider the dynamics of a model introduced recently by Bialas, Burda and
Johnston. At equilibrium the model exhibits a transition between a fluid and a
condensed phase. For long evolution times the dynamics of condensation
possesses a scaling regime that we study by analytical and numerical means. We
determine the scaling form of the occupation number probabilities. The
behaviour of the two-time correlations of the energy demonstrates that aging
takes place in the condensed phase, while it does not in the fluid phase.Comment: 8 pages, plain tex, 2 figure
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