774 research outputs found
Numerical studies of the two- and three-dimensional gauge glass at low temperature
We present results from Monte Carlo simulations of the two- and
three-dimensional gauge glass at low temperature using the parallel tempering
Monte Carlo method. Our results in two dimensions strongly support the
transition being at T_c=0. A finite-size scaling analysis, which works well
only for the larger sizes and lower temperatures, gives the stiffness exponent
theta = -0.39 +/- 0.03. In three dimensions we find theta = 0.27 +/- 0.01,
compatible with recent results from domain wall renormalization group studies.Comment: 7 pages, 10 figures, submitted to PR
Monte Carlo simulations of the four-dimensional XY spin glass at low temperatures
We report results for simulations of the four-dimensional XY spin glass using
the parallel tempering Monte Carlo method at low temperatures for moderate
sizes. Our results are qualitatively consistent with earlier work on the
three-dimensional gauge glass as well as three- and four-dimensional
Edwards-Anderson Ising spin glass. An extrapolation of our results would
indicate that large-scale excitations cost only a finite amount of energy in
the thermodynamic limit. The surface of these excitations may be fractal,
although we cannot rule out a scenario compatible with replica symmetry
breaking in which the surface of low-energy large-scale excitations is space
filling.Comment: 6 pages, 8 figure
On the existence of a finite-temperature transition in the two-dimensional gauge glass
Results from Monte Carlo simulations of the two-dimensional gauge glass
supporting a zero-temperature transition are presented. A finite-size scaling
analysis of the correlation length shows that the system does not exhibit
spin-glass order at finite temperatures. These results are compared to earlier
claims of a finite-temperature transition.Comment: 4 pages, 2 figure
Spin Glass Ordering in Diluted Magnetic Semiconductors: a Monte Carlo Study
We study the temperature-dilution phase diagram of a site-diluted Heisenberg
antiferromagnet on a fcc lattice, with and without the Dzyaloshinskii-Moriya
anisotropic term, fixed to realistic microscopic parameters for (IIB=Cd, Hg, Zn). We show that the dipolar Dzyaloshinskii-Moriya anisotropy
induces a finite-temperature phase transition to a spin glass phase, at
dilutions larger than 80%. The resulting probability distribution of the order
parameter P(q) is similar to the one found in the cubic lattice
Edwards-Anderson Ising model. The critical exponents undergo large finite size
corrections, but tend to values similar to the ones of the
Edwards-Anderson-Ising model.Comment: 4 pages plus 3 postscript figure
High-precision determination of the critical exponents for the lambda-transition of 4He by improved high-temperature expansion
We determine the critical exponents for the XY universality class in three
dimensions, which is expected to describe the -transition in He.
They are obtained from the analysis of high-temperature series computed for a
two-component model. The parameter is fixed such that
the leading corrections to scaling vanish. We obtain ,
, . These estimates improve previous
theoretical determinations and agree with the more precise experimental results
for liquid Helium.Comment: 8 pages, revte
Zero Temperature Glass Transition in the Two-Dimensional Gauge Glass Model
We investigate dynamic scaling properties of the two-dimensional gauge glass
model for the vortex glass phase in superconductors with quenched disorder.
From extensive Monte Carlo simulations we obtain static and dynamic finite
size scaling behavior, where the static simulations use a temperature exchange
method to ensure convergence at low temperatures. Both static and dynamic
scaling of Monte Carlo data is consistent with a glass transition at zero
temperature. We study a dynamic correlation function for the superconducting
order parameter, as well as the phase slip resistance. From the scaling of
these two functions, we find evidence for two distinct diverging correlation
times at the zero temperature glass transition. The longer of these time scales
is associated with phase slip fluctuations across the system that lead to
finite resistance at any finite temperature, while the shorter time scale is
associated with local phase fluctuations.Comment: 8 pages, 10 figures; v2: some minor correction
25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice
25th-order high-temperature series are computed for a general
nearest-neighbor three-dimensional Ising model with arbitrary potential on the
simple cubic lattice. In particular, we consider three improved potentials
characterized by suppressed leading scaling corrections. Critical exponents are
extracted from high-temperature series specialized to improved potentials,
obtaining , , ,
, , . Moreover, biased
analyses of the 25th-order series of the standard Ising model provide the
estimate for the exponent associated with the leading scaling
corrections. By the same technique, we study the small-magnetization expansion
of the Helmholtz free energy. The results are then applied to the construction
of parametric representations of the critical equation of state, using a
systematic approach based on a global stationarity condition. Accurate
estimates of several universal amplitude ratios are also presented.Comment: 40 pages, 15 figure
Low Energy Excitations in Spin Glasses from Exact Ground States
We investigate the nature of the low-energy, large-scale excitations in the
three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and
free boundary conditions, by studying the response of the ground state to a
coupling-dependent perturbation introduced previously. The ground states are
determined exactly for system sizes up to 12^3 spins using a branch and cut
algorithm. The data are consistent with a picture where the surface of the
excitations is not space-filling, such as the droplet or the ``TNT'' picture,
with only minimal corrections to scaling. When allowing for very large
corrections to scaling, the data are also consistent with a picture with
space-filling surfaces, such as replica symmetry breaking. The energy of the
excitations scales with their size with a small exponent \theta', which is
compatible with zero if we allow moderate corrections to scaling. We compare
the results with data for periodic boundary conditions obtained with a genetic
algorithm, and discuss the effects of different boundary conditions on
corrections to scaling. Finally, we analyze the performance of our branch and
cut algorithm, finding that it is correlated with the existence of
large-scale,low-energy excitations.Comment: 18 Revtex pages, 16 eps figures. Text significantly expanded with
more discussion of the numerical data. Fig.11 adde
Smeared phase transition in a three-dimensional Ising model with planar defects: Monte-Carlo simulations
We present results of large-scale Monte Carlo simulations for a
three-dimensional Ising model with short range interactions and planar defects,
i.e., disorder perfectly correlated in two dimensions. We show that the phase
transition in this system is smeared, i.e., there is no single critical
temperature, but different parts of the system order at different temperatures.
This is caused by effects similar to but stronger than Griffiths phenomena. In
an infinite-size sample there is an exponentially small but finite probability
to find an arbitrary large region devoid of impurities. Such a rare region can
develop true long-range order while the bulk system is still in the disordered
phase. We compute the thermodynamic magnetization and its finite-size effects,
the local magnetization, and the probability distribution of the ordering
temperatures for different samples. Our Monte-Carlo results are in good
agreement with a recent theory based on extremal statistics.Comment: 9 pages, 6 eps figures, final version as publishe
- …