294 research outputs found
Magnetic field relaxation in ferromagnetic Ising systems
We analyze the thermal magnetization reversal processes in magnetic grains.
Two experiments are carried out: swtiching time and switching field
experiments. In both cases, we find that the simulated behavior is coherent
with existing experimental data (the streched exponent of the switching time
experiment increases with the temperature and is superior to unity; there
exists a master curve for the switching field experiment). Moreover, we
simulated magnetic grains in a region of parameters where no experimental data
are available. We find that the relaxation time distribution is
gaussian, and we find the existence of a strong field regime.Comment: 9 pages, 7 figures, J.M.M.
SUE: A Special Purpose Computer for Spin Glass Models
The use of last generation Programmable Electronic Components makes possible
the construction of very powerful and competitive special purpose computers. We
have designed, constructed and tested a three-dimensional Spin Glass model
dedicated machine, which consists of 12 identical boards. Each single board can
simulate 8 different systems, updating all the systems at every clock cycle.
The update speed of the whole machine is 217ps/spin with 48 MHz clock
frequency. A device devoted to fast random number generation has been developed
and included in every board. The on-board reprogrammability permits us to
change easily the lattice size, or even the update algorithm or the action. We
present here a detailed description of the machine and the first runs using the
Heat Bath algorithm.Comment: Submitted to Computer Physics Communications, 19 pages, 5 figures,
references adde
Monte Carlo Simulation of the Three-dimensional Ising Spin Glass
We study the 3D 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. Using an iterative
extrapolation procedure, Monte Carlo data are extrapolated to infinite volume
up to correlation length \xi = 140. The infinite volume data are consistent
with both a continuous phase transition at finite temperature and an essential
singularity at finite temperature. An essential singularity at zero temperature
is excluded.Comment: 5 pages, 6 figures. Proceedings of the Workshop "Computer Simulation
Studies in Condensed Matter Physics XII", Eds. D.P. Landau, S.P. Lewis, and
H.B. Schuettler, (Springer Verlag, Heidelberg, Berlin, 1999
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
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
Ground state structure of diluted antiferromagnets and random field systems
A method is presented for the calculation of all exact ground states of
diluted antiferromagnets and random field systems in an arbitrary range of
fields. It works by calculating all jump-fields B,\Delta where the system
changes it's ground state. For each field value all degenerated ground states
are represented by a set of (anti-) ferromagnetic clusters and a relation
between the clusters. So a complete description of the ground state structure
of these systems is possible.
Systems are investigated up to size 48^3 on the whole field-range and up to
160^3 for some particular fields. The behavior of order parameters is
investigated, the number of jumps is analyzed and the degree of degeneracy as
functions of size and fields is calculated.Comment: 11 pages, 13 figures, LaTex, submitted to Physica
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
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
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
Universality in short-range Ising spin glasses
The role of the distribution of coupling constants on the critical exponents
of the short-range Ising spin-glass model is investigated via real space
renormalization group. A saddle-point spin glass critical point characterized
by a fixed-point distribution is found in an appropriated parameter space. The
critical exponents and are directly estimated from the data of
the local Edwards-Anderson order parameters for the model defined on a diamond
hierarchical lattice of fractal dimension . Four distinct initial
distributions of coupling constants (Gaussian, bimodal, uniform and
exponential) are considered; the results clearly indicate a universal behavior.Comment: 11 pages, 4 figures, to published in Physica A 199
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