1,234 research outputs found
Conformal invariance and linear defects in the two-dimensional Ising model
Using conformal invariance, we show that the non-universal exponent eta_0
associated with the decay of correlations along a defect line of modified bonds
in the square-lattice Ising model is related to the amplitude A_0=xi_n/n of the
correlation length \xi_n(K_c) at the bulk critical coupling K_c, on a strip
with width n, periodic boundary conditions and two equidistant defect lines
along the strip, through A_0=(\pi\eta_0)^{-1}.Comment: Old paper, for archiving. 5 pages, 4 figures, IOP macro, eps
Fisher Renormalization for Logarithmic Corrections
For continuous phase transitions characterized by power-law divergences,
Fisher renormalization prescribes how to obtain the critical exponents for a
system under constraint from their ideal counterparts. In statistical
mechanics, such ideal behaviour at phase transitions is frequently modified by
multiplicative logarithmic corrections. Here, Fisher renormalization for the
exponents of these logarithms is developed in a general manner. As for the
leading exponents, Fisher renormalization at the logarithmic level is seen to
be involutory and the renormalized exponents obey the same scaling relations as
their ideal analogs. The scheme is tested in lattice animals and the Yang-Lee
problem at their upper critical dimensions, where predictions for logarithmic
corrections are made.Comment: 10 pages, no figures. Version 2 has added reference
Critical phenomena on scale-free networks: logarithmic corrections and scaling functions
In this paper, we address the logarithmic corrections to the leading power
laws that govern thermodynamic quantities as a second-order phase transition
point is approached. For phase transitions of spin systems on d-dimensional
lattices, such corrections appear at some marginal values of the order
parameter or space dimension. We present new scaling relations for these
exponents. We also consider a spin system on a scale-free network which
exhibits logarithmic corrections due to the specific network properties. To
this end, we analyze the phase behavior of a model with coupled order
parameters on a scale-free network and extract leading and logarithmic
correction-to-scaling exponents that determine its field- and temperature
behavior. Although both non-trivial sets of exponents emerge from the
correlations in the network structure rather than from the spin fluctuations
they fulfil the respective thermodynamic scaling relations. For the scale-free
networks the logarithmic corrections appear at marginal values of the node
degree distribution exponent. In addition we calculate scaling functions, which
also exhibit nontrivial dependence on intrinsic network properties.Comment: 15 pages, 4 figure
Bond-disordered Anderson model on a two dimensional square lattice - chiral symmetry and restoration of one-parameter scaling
Bond-disordered Anderson model in two dimensions on a square lattice is
studied numerically near the band center by calculating density of states
(DoS), multifractal properties of eigenstates and the localization length. DoS
divergence at the band center is studied and compared with Gade's result [Nucl.
Phys. B 398, 499 (1993)] and the powerlaw. Although Gade's form describes
accurately DoS of finite size systems near the band-center, it fails to
describe the calculated part of DoS of the infinite system, and a new
expression is proposed. Study of the level spacing distributions reveals that
the state closest to the band center and the next one have different level
spacing distribution than the pairs of states away from the band center.
Multifractal properties of finite systems furthermore show that scaling of
eigenstates changes discontinuously near the band center. This unusual behavior
suggests the existence of a new divergent length scale, whose existence is
explained as the finite size manifestation of the band center critical point of
the infinite system, and the critical exponent of the correlation length is
calculated by a finite size scaling. Furthermore, study of scaling of Lyapunov
exponents of transfer matrices of long stripes indicates that for a long stripe
of any width there is an energy region around band center within which the
Lyapunov exponents cannot be described by one-parameter scaling. This region,
however, vanishes in the limit of the infinite square lattice when
one-parameter scaling is restored, and the scaling exponent calculated, in
agreement with the result of the finite size scaling analysis.Comment: 23 pages, 11 figures. RevTe
Computer simulation of the critical behavior of 3D disordered Ising model
The critical behavior of the disordered ferromagnetic Ising model is studied
numerically by the Monte Carlo method in a wide range of variation of
concentration of nonmagnetic impurity atoms. The temperature dependences of
correlation length and magnetic susceptibility are determined for samples with
various spin concentrations and various linear sizes. The finite-size scaling
technique is used for obtaining scaling functions for these quantities, which
exhibit a universal behavior in the critical region; the critical temperatures
and static critical exponents are also determined using scaling corrections. On
the basis of variation of the scaling functions and values of critical
exponents upon a change in the concentration, the conclusion is drawn
concerning the existence of two universal classes of the critical behavior of
the diluted Ising model with different characteristics for weakly and strongly
disordered systems.Comment: 14 RevTeX pages, 6 figure
A Farewell to Liouvillians
We examine the Liouvillian approach to the quantum Hall plateau transition,
as introduced recently by Sinova, Meden, and Girvin [Phys. Rev. B {\bf 62},
2008 (2000)] and developed by Moore, Sinova and Zee [Phys. Rev. Lett. {\bf 87},
046801 (2001)]. We show that, despite appearances to the contrary, the
Liouvillian approach is not specific to the quantum mechanics of particles
moving in a single Landau level: we formulate it for a general disordered
single-particle Hamiltonian. We next examine the relationship between
Liouvillian perturbation theory and conventional calculations of
disorder-averaged products of Green functions and show that each term in
Liouvillian perturbation theory corresponds to a specific contribution to the
two-particle Green function. As a consequence, any Liouvillian approximation
scheme may be re-expressed in the language of Green functions. We illustrate
these ideas by applying Liouvillian methods, including their extension to Liouvillian flavors, to random matrix ensembles, using numerical
calculations for small integer and an analytic analysis for large .
We find that behavior at is different in qualitative ways from that
at . In particular, the limit expressed using Green
functions generates a pathological approximation, in which two-particle
correlation functions fail to factorize correctly at large separations of their
energy, and exhibit spurious singularities inside the band of random matrix
energy levels. We also consider the large treatment of the quantum Hall
plateau transition, showing that the same undesirable features are present
there, too
Diagrammatic analysis of the two-state quantum Hall system with chiral invariance
The quantum Hall system in the lowest Landau level with Zeeman term is
studied by a two-state model, which has a chiral invariance. Using a
diagrammatic analysis, we examine this two-state model with random impurity
scattering, and find the exact value of the conductivity at the Zeeman energy
. We further study the conductivity at the another extended state
(). We find that the values of the conductivities at
and do not depend upon the value of the Zeeman energy
. We discuss also the case where the Zeeman energy becomes a
random field.Comment: 14P, Late
Passive scalars, random flux, and chiral phase fluids
We study the two-dimensional localization problem for (i) a classical
diffusing particle advected by a quenched random mean-zero vorticity field, and
(ii) a quantum particle in a quenched random mean-zero magnetic field. Through
a combination of numerical and analytic techniques we argue that both systems
have extended eigenstates at a special point in the spectrum, , where a
sublattice decomposition obtains. In a neighborhood of this point, the Lyapunov
exponents of the transfer-matrices acquire ratios characteristic of conformal
invariance allowing an indirect determination of for the typical spatial
decay of eigenstates.Comment: use revtex, two-column, 4 pages, 5 postscript figures, submitted to
PR
Epstein-Barr virus (EBV) deletions as biomarkers of response to treatment of chronic active EBV
Chronic active Epstein–Barr virus (CAEBV) disease is a rare condition characterised by persistent EBV infection in previously healthy individuals. Defective EBV genomes were found in East Asian patients with CAEBV. In the present study, we sequenced 14 blood EBV samples from three UK patients with CAEBV, comparing the results with saliva CAEBV samples and other conditions. We observed EBV deletions in blood, some of which may disrupt viral replication, but not saliva in CAEBV. Deletions were lost overtime after successful treatment. These findings are compatible with CAEBV being associated with the evolution and persistence of EBV+ haematological clones that are lost on successful treatment
Strong Coupling Fixed Points of Current Interactions and Disordered Fermions in 2D
The all-orders beta function is used to study disordered Dirac fermions in
2D. The generic strong coupling fixed `points' of anisotropic current-current
interactions at large distances are actually isotropic manifolds corresponding
to subalgebras of the maximal current algebra at short distances. The IR
theories are argued to be current algebra cosets. We illustrate this with the
simple example of anisotropic su(2), which is the physics of
Kosterlitz-Thouless transitions. We work out the phase diagram for the
Chalker-Coddington network model which is in the universality class of the
integer Quantum Hall transition. One massless phase is in the universality
class of dense polymers.Comment: published version (Phys. Rev. B
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