Accurate Estimates of 3D Ising Critical Exponents Using the Coherent-Anomaly Method

An analysis of the critical behavior of the three-dimensional Ising model using the coherent-anomaly method (CAM) is presented. Various sources of errors in CAM estimates of critical exponents are discussed, and an improved scheme for the CAM data analysis is tested. Using a set of mean-field type approximations based on the variational series expansion approach, accuracy comparable to the most precise conventional methods has been achieved. Our results for the critical exponents are given by \alpha=\afin, \beta=\bfin, \gamma=\gfin and \delta=\dfin.Comment: 16 pages, latex, 1 postscript figur

A comment on free-fermion conditions for lattice models in two and more dimensions

We analyze free-fermion conditions on vertex models. We show --by examining examples of vertex models on square, triangular, and cubic lattices-- how they amount to degeneration conditions for known symmetries of the Boltzmann weights, and propose a general scheme for such a process in two and more dimensions.Comment: 12 pages, plain Late

CRITICAL EXPONENTS OF THE 3D ANTIFERROMAGNETIC THREE-STATE POTTS MODEL USING THE COHERENT-ANOMALY METHOD

The antiferromagnetic three-state Potts model on the simple-cubic lattice is studied using the coherent-anomaly method (CAM). The CAM analysis provides the estimates for the critical exponents which indicate the XY universality class, namely $\alpha=-0.011$, $\beta= 0.351$, $\gamma= 1.309$ and $\delta= 4.73$. This observation corroborates the results of the recent Monte Carlo simulations, and disagrees with the proposal of a new universality class.Comment: 11 pages, latex, 1 postscript figure, changes: an incorrect reference omitte

Approximating the leading singular triplets of a large matrix function

Given a large square matrix $A$ and a sufficiently regular function $f$ so that $f(A)$ is well defined, we are interested in the approximation of the leading singular values and corresponding singular vectors of $f(A)$, and in particular of $\|f(A)\|$, where $\|\cdot \|$ is the matrix norm induced by the Euclidean vector norm. Since neither $f(A)$ nor $f(A)v$ can be computed exactly, we introduce and analyze an inexact Golub-Kahan-Lanczos bidiagonalization procedure, where the inexactness is related to the inaccuracy of the operations $f(A)v$, $f(A)^*v$. Particular outer and inner stopping criteria are devised so as to cope with the lack of a true residual. Numerical experiments with the new algorithm on typical application problems are reported

Process for the preparation of catalytically active cross-linked metal silicate

Highly active and selective hydroisomerization catalysts are prepared by heating to 300 DEG -450 DEG C. at subatmospheric pressure, a mixture of nickel synthetic mica montmorillonite (Ni-SMM) with a hydroxy aluminum polymeric solution. The resulting pillared Ni-SMM catalyst, preferably Pd-loaded, is especially useful in hydroisomerizing C4-C7 paraffins

Random Matrix Theory and Classical Statistical Mechanics. I. Vertex Models

A connection between integrability properties and general statistical properties of the spectra of symmetric transfer matrices of the asymmetric eight-vertex model is studied using random matrix theory (eigenvalue spacing distribution and spectral rigidity). For Yang-Baxter integrable cases, including free-fermion solutions, we have found a Poissonian behavior, whereas level repulsion close to the Wigner distribution is found for non-integrable models. For the asymmetric eight-vertex model, however, the level repulsion can also disappearand the Poisson distribution be recovered on (non Yang--Baxter integrable) algebraic varieties, the so-called disorder varieties. We also present an infinite set of algebraic varieties which are stable under the action of an infinite discrete symmetry group of the parameter space. These varieties are possible loci for free parafermions. Using our numerical criterion we have tested the generic calculability of the model on these algebraic varieties.Comment: 25 pages, 7 PostScript Figure

Nonlinear cochlear dynamics

In this report we examine a model for human hearing. The unknown parameters in the model are estimated using experimental data and standard optimisation methods as described in the text. Additionally, we suggest possible improvements to the model as well as proposing a method to use the current model in locating which frequencies are aected in a damaged ear. Keywords: cochlear model, delay dierential equation, parameter es-timation, hearing los