67 research outputs found
New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain
In this paper we show how an infinite system of coupled Toda-type nonlinear
differential equations derived by one of us can be used efficiently to
calculate the time-dependent pair-correlations in the Ising chain in a
transverse field. The results are seen to match extremely well long large-time
asymptotic expansions newly derived here. For our initial conditions we use new
long asymptotic expansions for the equal-time pair correlation functions of the
transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising
model. Using this one can also study the equal-time wavevector-dependent
correlation function of the quantum chain, a.k.a. the q-dependent diagonal
susceptibility in the 2d Ising model, in great detail with very little
computational effort.Comment: LaTeX 2e, 31 pages, 8 figures (16 eps files). vs2: Two references
added and minor changes of style. vs3: Corrections made and reference adde
Scaling fields in the two-dimensional abelian sandpile model
We consider the isotropic two-dimensional abelian sandpile model from a
perspective based on two-dimensional (conformal) field theory. We compute
lattice correlation functions for various cluster variables (at and off
criticality), from which we infer the field-theoretic description in the
scaling limit. We find a perfect agreement with the predictions of a c=-2
conformal field theory and its massive perturbation, thereby providing direct
evidence for conformal invariance and more generally for a description in terms
of a local field theory. The question of the height 2 variable is also
addressed, with however no definite conclusion yet.Comment: 22 pages, 1 figure (eps), uses revte
Competing interactions in the XYZ model
We study the interplay between a XY anisotropy , exchange modulations
and an external magnetic field along the z direction in the XYZ chain using
bosonization and Lanczos diagonalization techniques. We find an Ising critical
line in the space of couplings which occur due to competing relevant
perturbations which are present. More general situations are also discussed.Comment: 6 pages, 6 figure
Random walks and polymers in the presence of quenched disorder
After a general introduction to the field, we describe some recent results
concerning disorder effects on both `random walk models', where the random walk
is a dynamical process generated by local transition rules, and on `polymer
models', where each random walk trajectory representing the configuration of a
polymer chain is associated to a global Boltzmann weight. For random walk
models, we explain, on the specific examples of the Sinai model and of the trap
model, how disorder induces anomalous diffusion, aging behaviours and Golosov
localization, and how these properties can be understood via a strong disorder
renormalization approach. For polymer models, we discuss the critical
properties of various delocalization transitions involving random polymers. We
first summarize some recent progresses in the general theory of random critical
points : thermodynamic observables are not self-averaging at criticality
whenever disorder is relevant, and this lack of self-averaging is directly
related to the probability distribution of pseudo-critical temperatures
over the ensemble of samples of size . We describe the
results of this analysis for the bidimensional wetting and for the
Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S.,
France, November 200
Risk-Stratified Management to Remove Low-Risk Penicillin Allergy Labels in the Patients with COVID-19 in the Intensive Care Unit
FINITE BATH ADSORPTION OF β-GALACTOSIDASE ONTO MONOCLONAL ANTIBODY LIGAND IMMOBILIZED ON NONPOROUS GLASS COATED BEADS
Laser induced incandescence measurements of soot volume fraction and effective particle size in a laminar co-annular non-premixed methane/air flame at pressures between 0.5–4.0 MPa
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