1,192 research outputs found
Monte Carlo study of the scaling of universal correlation lengths in three-dimensional O(n) spin models
Using an elaborate set of simulational tools and statistically optimized
methods of data analysis we investigate the scaling behavior of the correlation
lengths of three-dimensional classical O() spin models. Considering
three-dimensional slabs , the results over a
wide range of indicate the validity of special scaling relations involving
universal amplitude ratios that are analogous to results of conformal field
theory for two-dimensional systems. A striking mismatch of the
extrapolation of these simulations against analytical calculations is traced
back to a breakdown of the identification of this limit with the spherical
model.Comment: 18 pages, 9 figures, REVTeX4, slightly shortened, updated critical
exponent estimate
Universal amplitude ratios in finite-size scaling: three-dimensional Ising model
Motivated by the results of two-dimensional conformal field theory (CFT) we
investigate the finite-size scaling of the mass spectrum of an Ising model on
three-dimensional lattices with a spherical cross section. Using a
cluster-update Monte Carlo technique we find a linear relation between the
masses and the corresponding scaling dimensions, in complete analogy to the
situation in two dimensions. Amplitude ratios as well as the amplitudes
themselves appear to be universal in this case.Comment: 3 pages, 2 figures, proceedings of LATTICE99, Pis
Spin and chiral stiffness of the XY spin glass in two dimensions
We analyze the zero-temperature behavior of the XY Edwards-Anderson spin
glass model on a square lattice. A newly developed algorithm combining exact
ground-state computations for Ising variables embedded into the planar spins
with a specially tailored evolutionary method, resulting in the genetic
embedded matching (GEM) approach, allows for the computation of numerically
exact ground states for relatively large systems. This enables a thorough
re-investigation of the long-standing questions of (i) extensive degeneracy of
the ground state and (ii) a possible decoupling of spin and chiral degrees of
freedom in such systems. The new algorithm together with appropriate choices
for the considered sets of boundary conditions and finite-size scaling
techniques allows for a consistent determination of the spin and chiral
stiffness scaling exponents.Comment: 6 pages, 2 figures, proceedings of the HFM2006 conference, to appear
in a special issue of J. Phys.: Condens. Matte
Domain-wall excitations in the two-dimensional Ising spin glass
The Ising spin glass in two dimensions exhibits rich behavior with subtle
differences in the scaling for different coupling distributions. We use
recently developed mappings to graph-theoretic problems together with highly
efficient implementations of combinatorial optimization algorithms to determine
exact ground states for systems on square lattices with up to spins. While these mappings only work for planar graphs, for example
for systems with periodic boundary conditions in at most one direction, we
suggest here an iterative windowing technique that allows one to determine
ground states for fully periodic samples up to sizes similar to those for the
open-periodic case. Based on these techniques, a large number of disorder
samples are used together with a careful finite-size scaling analysis to
determine the stiffness exponents and domain-wall fractal dimensions with
unprecedented accuracy, our best estimates being and
for Gaussian couplings. For bimodal disorder, a
new uniform sampling algorithm allows us to study the domain-wall fractal
dimension, finding . Additionally, we also investigate
the distributions of ground-state energies, of domain-wall energies, and
domain-wall lengths.Comment: 19 pages, 12 figures, 5 tables, accepted versio
Cluster Percolation in the Two-Dimensional Ising Spin Glass
Suitable cluster definitions have allowed researchers to describe many
ordering transitions in spin systems as geometric phenomena related to
percolation. For spin glasses and some other systems with quenched disorder,
however, such a connection is missing to date. Using Monte Carlo simulations,
we study the percolation properties of several classes of clusters occurring in
the Edwards-Anderson Ising spin-glass model in two dimensions. The
Fortuin-Kasteleyn-Coniglio-Klein clusters originally defined for the
ferromagnetic problem do percolate at a temperature that remains non-zero in
the thermodynamic limit. On the Nishimori line, this location is accurately
predicted by an argument due to Yamaguchi. More relevant for the spin-glass
transition are clusters defined on the basis of the overlap of several
replicas. We show that various such cluster types have percolation thresholds
that shift to lower temperature by increasing the system size, in agreement
with the zero-temperature spin-glass transition in two dimensions. The overlap
is linked to the difference in density of the two largest clusters, thus
supporting a picture where the spin-glass transition corresponds to an emergent
density difference of the two largest clusters inside the percolating phase.Comment: 14 pages, 18 figures, 1 table, RevTeX 4.
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