18 research outputs found
Explicit Renormalization Group for D=2 random bond Ising model with long-range correlated disorder
We investigate the explicit renormalization group for fermionic field
theoretic representation of two-dimensional random bond Ising model with
long-range correlated disorder. We show that a new fixed point appears by
introducing a long-range correlated disorder. Such as the one has been observed
in previous works for the bosonic () description. We have calculated
the correlation length exponent and the anomalous scaling dimension of
fermionic fields at this fixed point. Our results are in agreement with the
extended Harris criterion derived by Weinrib and Halperin.Comment: 5 page
Correlation decay and conformal anomaly in the two-dimensional random-bond Ising ferromagnet
The two-dimensional random-bond Ising model is numerically studied on long
strips by transfer-matrix methods. It is shown that the rate of decay of
correlations at criticality, as derived from averages of the two largest
Lyapunov exponents plus conformal invariance arguments, differs from that
obtained through direct evaluation of correlation functions. The latter is
found to be, within error bars, the same as in pure systems. Our results
confirm field-theoretical predictions. The conformal anomaly is calculated
from the leading finite-width correction to the averaged free energy on strips.
Estimates thus obtained are consistent with , the same as for the pure
Ising model.Comment: RevTeX 3, 11 pages +2 figures, uuencoded, IF/UFF preprin
How to remove the boundary in CFT - an operator algebraic procedure
The relation between two-dimensional conformal quantum field theories with
and without a timelike boundary is explored.Comment: 18 pages, 2 figures. v2: more precise title, reference correcte
Ising cubes with enhanced surface couplings
Using Monte Carlo techniques, Ising cubes with ferromagnetic nearest-neighbor
interactions and enhanced couplings between surface spins are studied. In
particular, at the surface transition, the corner magnetization shows
non-universal, coupling-dependent critical behavior in the thermodynamic limit.
Results on the critical exponent of the corner magnetization are compared to
previous findings on two-dimensional Ising models with three intersecting
defect lines.Comment: 4 pages, 2 figures included, submitted to Phys. Rev.
Order Parameters of the Dilute A Models
The free energy and local height probabilities of the dilute A models with
broken \Integer_2 symmetry are calculated analytically using inversion and
corner transfer matrix methods. These models possess four critical branches.
The first two branches provide new realisations of the unitary minimal series
and the other two branches give a direct product of this series with an Ising
model. We identify the integrable perturbations which move the dilute A models
away from the critical limit. Generalised order parameters are defined and
their critical exponents extracted. The associated conformal weights are found
to occur on the diagonal of the relevant Kac table. In an appropriate regime
the dilute A model lies in the universality class of the Ising model in a
magnetic field. In this case we obtain the magnetic exponent
directly, without the use of scaling relations.Comment: 53 pages, LaTex, ITFA 93-1
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
Fermionic SK-models with Hubbard interaction: Magnetism and electronic structure
Models with range-free frustrated Ising spin- and Hubbard interaction are
treated exactly by means of the discrete time slicing method. Critical and
tricritical points, correlations, and the fermion propagator, are derived as a
function of temperature T, chemical potential \mu, Hubbard coupling U, and spin
glass energy J. The phase diagram is obtained. Replica symmetry breaking
(RSB)-effects are evaluated up to four-step order (4RSB). The use of exact
relations together with the 4RSB-solutions allow to model exact solutions by
interpolation. For T=0, our numerical results provide strong evidence that the
exact density of states in the spin glass pseudogap regime obeys \rho(E)=const
|E-E_F| for energies close to the Fermi level. Rapid convergence of \rho'(E_F)
under increasing order of RSB is observed. The leading term resembles the
Efros-Shklovskii Coulomb pseudogap of localized disordered fermionic systems in
2D. Beyond half filling we obtain a quadratic dependence of the fermion filling
factor on the chemical potential. We find a half filling transition between a
phase for U>\mu, where the Fermi level lies inside the Hubbard gap, into a
phase where \mu(>U) is located at the center of the upper spin glass pseudogap
(SG-gap). For \mu>U the Hubbard gap combines with the lower one of two SG-gaps
(phase I), while for \mu<U it joins the sole SG-gap of the half-filling regime
(phase II). We predict scaling behaviour at the continuous half filling
transition. Implications of the half-filling transition between the deeper
insulating phase II and phase I for delocalization due to hopping processes in
itinerant model extensions are discussed and metal-insulator transition
scenarios described.Comment: 29 pages, 26 Figures, 4 jpeg- and 3 gif-Fig-files include
Dynamically Driven Renormalization Group Applied to Sandpile Models
The general framework for the renormalization group analysis of
self-organized critical sandpile models is formulated. The usual real space
renormalization scheme for lattice models when applied to nonequilibrium
dynamical models must be supplemented by feedback relations coming from the
stationarity conditions. On the basis of these ideas the Dynamically Driven
Renormalization Group is applied to describe the boundary and bulk critical
behavior of sandpile models. A detailed description of the branching nature of
sandpile avalanches is given in terms of the generating functions of the
underlying branching process.Comment: 18 RevTeX pages, 5 figure
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