160 research outputs found
Asymptotic behavior of the density of states on a random lattice
We study the diffusion of a particle on a random lattice with fluctuating
local connectivity of average value q. This model is a basic description of
relaxation processes in random media with geometrical defects. We analyze here
the asymptotic behavior of the eigenvalue distribution for the Laplacian
operator. We found that the localized states outside the mobility band and
observed by Biroli and Monasson (1999, J. Phys. A: Math. Gen. 32 L255), in a
previous numerical analysis, are described by saddle point solutions that
breaks the rotational symmetry of the main action in the real space. The
density of states is characterized asymptotically by a series of peaks with
periodicity 1/q.Comment: 11 pages, 2 figure
Integrable Discretizations of Chiral Models
A construction of conservation laws for chiral models (generalized
sigma-models on a two-dimensional space-time continuum using differential forms
is extended in such a way that it also comprises corresponding discrete
versions. This is achieved via a deformation of the ordinary differential
calculus. In particular, the nonlinear Toda lattice results in this way from
the linear (continuum) wave equation. The method is applied to several further
examples. We also construct Lax pairs and B\"acklund transformations for the
class of models considered in this work.Comment: 14 pages, Late
Exchange Monte Carlo Method and Application to Spin Glass Simulations
We propose an efficient Monte Carlo algorithm for simulating a
``hardly-relaxing" system, in which many replicas with different temperatures
are simultaneously simulated and a virtual process exchanging configurations of
these replica is introduced. This exchange process is expected to let the
system at low temperatures escape from a local minimum. By using this algorithm
the three-dimensional Ising spin glass model is studied. The ergodicity
time in this method is found much smaller than that of the multi-canonical
method. In particular the time correlation function almost follows an
exponential decay whose relaxation time is comparable to the ergodicity time at
low temperatures. It suggests that the system relaxes very rapidly through the
exchange process even in the low temperature phase.Comment: 10 pages + uuencoded 5 Postscript figures, REVTe
Phase Transition in the Three-Dimensional Ising Spin Glass
We have studied the three-dimensional Ising spin glass with a
distribution by Monte Carlo simulations. Using larger sizes and much better
statistics than in earlier work, a finite size scaling analysis shows quite
strong evidence for a finite transition temperature, , with ordering below
. Our estimate of the transition temperature is rather lower than in
earlier work, and the value of the correlation length exponent, , is
somewhat higher. Because there may be (unknown) corrections to finite size
scaling, we do not completely rule out the possibility that or that
is finite but with no order below . However, from our data, these
possibilities seem less likely.Comment: Postscript file compressed using uufiles. The postscript file is also
available by anonymous ftp at ftp://chopin.ucsc.edu/pub/sg3d.p
Universal Finite Size Scaling Functions in the 3D Ising Spin Glass
We study the three-dimensional Edwards-Anderson model with binary
interactions by Monte Carlo simulations. Direct evidence of finite-size scaling
is provided, and the universal finite-size scaling functions are determined.
Monte Carlo data are extrapolated to infinite volume with an iterative
procedure up to correlation lengths xi \approx 140. The infinite volume data
are consistent with a conventional power law singularity at finite temperature
Tc. Taking into account corrections to scaling, we find Tc = 1.156 +/- 0.015,
nu = 1.8 +/- 0.2 and eta = -0.26 +/- 0.04. The data are also consistent with an
exponential singularity at finite Tc, but not with an exponential singularity
at zero temperature.Comment: 4 pages, Revtex, 4 postscript figures include
Monte Carlo Simulation of a Random-Field Ising Antiferromagnet
Phase transitions in the three-dimensional diluted Ising antiferromagnet in
an applied magnetic field are analyzed numerically. It is found that random
magnetic field in a system with spin concentration below a certain threshold
induces a crossover from second-order phase transition to first-order
transition to a new phase characterized by a spin-glass ground state and
metastable energy states at finite temperatures.Comment: 10 pages, 11 figure
Numerical Results for the Ground-State Interface in a Random Medium
The problem of determining the ground state of a -dimensional interface
embedded in a -dimensional random medium is treated numerically. Using a
minimum-cut algorithm, the exact ground states can be found for a number of
problems for which other numerical methods are inexact and slow. In particular,
results are presented for the roughness exponents and ground-state energy
fluctuations in a random bond Ising model. It is found that the roughness
exponent , with the related energy
exponent being , in ,
respectively. These results are compared with previous analytical and numerical
estimates.Comment: 10 pages, REVTEX3.0; 3 ps files (separate:tar/gzip/uuencoded) for
figure
Monte Carlo study of the random-field Ising model
Using a cluster-flipping Monte Carlo algorithm combined with a generalization
of the histogram reweighting scheme of Ferrenberg and Swendsen, we have studied
the equilibrium properties of the thermal random-field Ising model on a cubic
lattice in three dimensions. We have equilibrated systems of LxLxL spins, with
values of L up to 32, and for these systems the cluster-flipping method appears
to a large extent to overcome the slow equilibration seen in single-spin-flip
methods. From the results of our simulations we have extracted values for the
critical exponents and the critical temperature and randomness of the model by
finite size scaling. For the exponents we find nu = 1.02 +/- 0.06, beta = 0.06
+/- 0.07, gamma = 1.9 +/- 0.2, and gammabar = 2.9 +/- 0.2.Comment: 12 pages, 6 figures, self-expanding uuencoded compressed PostScript
fil
String Propagator: a Loop Space Representation
The string quantum kernel is normally written as a functional sum over the
string coordinates and the world--sheet metrics. As an alternative to this
quantum field--inspired approach, we study the closed bosonic string
propagation amplitude in the functional space of loop configurations. This
functional theory is based entirely on the Jacobi variational formulation of
quantum mechanics, {\it without the use of a lattice approximation}. The
corresponding Feynman path integral is weighed by a string action which is a
{\it reparametrization invariant} version of the Schild action. We show that
this path integral formulation is equivalent to a functional ``Schrodinger''
equation defined in loop--space. Finally, for a free string, we show that the
path integral and the functional wave equation are {\it exactly } solvable.Comment: 15 pages, no figures, ReVTeX 3.
Critical Exponents of the pure and random-field Ising models
We show that current estimates of the critical exponents of the
three-dimensional random-field Ising model are in agreement with the exponents
of the pure Ising system in dimension 3 - theta where theta is the exponent
that governs the hyperscaling violation in the random case.Comment: 9 pages, 4 encapsulated Postscript figures, REVTeX 3.
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