38 research outputs found
Nature of Phase Transitions in a Generalized Complex |psi|^4 Model
We employ Monte Carlo simulations to study a generalized three-dimensional
complex $psi|^4 theory of Ginzburg-Landau form and compare our numerical
results with a recent quasi-analytical mean-field type approximation, which
predicts first-order phase transitions in parts of the phase diagram. As we
have shown earlier, this approximation does not apply to the standard
formulation of the model. This motivated us to introduce a generalized
Hamiltonian with an additional fugacity term controlling implicitly the vortex
density. With this modification we find that the complex |psi|^4 theory can, in
fact, be tuned to undergo strong first-order phase transitions. The standard
model is confirmed to exhibit continuous transitions which can be characterized
by XY model exponents, as expected by universality arguments. A few remarks on
the two-dimensional case are also made.Comment: 11 pages, RevTex, 33 postscript figures, author information under
http://www.physik.uni-leipzig.de/index.php?id=2
Universal amplitudes in the FSS of three-dimensional spin models
In a MC study using a cluster update algorithm we investigate the finite-size
scaling (FSS) of the correlation lengths of several representatives of the
class of three-dimensional classical O(n) symmetric spin models on a column
geometry. For all considered models we find strong evidence for a linear
relation between FSS amplitudes and scaling dimensions when applying
antiperiodic instead of periodic boundary conditions across the torus. The
considered type of scaling relation can be proven analytically for systems on
two-dimensional strips with periodic bc using conformal field theoryComment: 4 pages, RevTex, uses amsfonts.sty, 3 Figure
Critical Exponents of the Classical 3D Heisenberg Model: A Single-Cluster Monte Carlo Study
We have simulated the three-dimensional Heisenberg model on simple cubic
lattices, using the single-cluster Monte Carlo update algorithm. The expected
pronounced reduction of critical slowing down at the phase transition is
verified. This allows simulations on significantly larger lattices than in
previous studies and consequently a better control over systematic errors. In
one set of simulations we employ the usual finite-size scaling methods to
compute the critical exponents from a few
measurements in the vicinity of the critical point, making extensive use of
histogram reweighting and optimization techniques. In another set of
simulations we report measurements of improved estimators for the spatial
correlation length and the susceptibility in the high-temperature phase,
obtained on lattices with up to spins. This enables us to compute
independent estimates of and from power-law fits of their
critical divergencies.Comment: 33 pages, 12 figures (not included, available on request). Preprint
FUB-HEP 19/92, HLRZ 77/92, September 199
The Harris-Luck criterion for random lattices
The Harris-Luck criterion judges the relevance of (potentially) spatially
correlated, quenched disorder induced by, e.g., random bonds, randomly diluted
sites or a quasi-periodicity of the lattice, for altering the critical behavior
of a coupled matter system. We investigate the applicability of this type of
criterion to the case of spin variables coupled to random lattices. Their
aptitude to alter critical behavior depends on the degree of spatial
correlations present, which is quantified by a wandering exponent. We consider
the cases of Poissonian random graphs resulting from the Voronoi-Delaunay
construction and of planar, ``fat'' Feynman diagrams and precisely
determine their wandering exponents. The resulting predictions are compared to
various exact and numerical results for the Potts model coupled to these
quenched ensembles of random graphs.Comment: 13 pages, 9 figures, 2 tables, REVTeX 4. Version as published, one
figure added for clarification, minor re-wordings and typo cleanu
Ising model on 3D random lattices: A Monte Carlo study
We report single-cluster Monte Carlo simulations of the Ising model on
three-dimensional Poissonian random lattices with up to 128,000 approx. 503
sites which are linked together according to the Voronoi/Delaunay prescription.
For each lattice size quenched averages are performed over 96 realizations. By
using reweighting techniques and finite-size scaling analyses we investigate
the critical properties of the model in the close vicinity of the phase
transition point. Our random lattice data provide strong evidence that, for the
available system sizes, the resulting effective critical exponents are
indistinguishable from recent high-precision estimates obtained in Monte Carlo
studies of the Ising model and \phi^4 field theory on three-dimensional regular
cubic lattices.Comment: 35 pages, LaTex, 8 tables, 8 postscript figure