Numerical Results For The 2D Random Bond 3-state Potts Model

We present results of a numerical simulation of the 3-state Potts model with random bond, in two dimension. In particular, we measure the critical exponent associated to the magnetization and the specific heat. We also compare these exponents with recent analytical computations.Comment: 9 pages, latex, 3 Postscript figure

Scaling and finte-size-scaling in the two dimensional random-coupling Ising ferromagnet

It is shown by Monte Carlo method that the finite size scaling (FSS) holds in the two dimensional random-coupled Ising ferromagnet. It is also demonstrated that the form of universal FSS function constructed via novel FSS scheme depends on the strength of the random coupling for strongly disordered cases. Monte Carlo measurements of thermodynamic (infinite volume limit) data of the correlation length ($\xi$) up to $\xi \simeq 200$ along with measurements of the fourth order cumulant ratio (Binder's ratio) at criticality are reported and analyzed in view of two competing scenarios. It is demonstrated that the data are almost exclusively consistent with the scenario of weak universality.Comment: 9 pages, 4figuer

Crossover and self-averaging in the two-dimensional site-diluted Ising model

Using the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm, we simulate the two-dimensional (2D) site-diluted Ising model. Since we can tune the critical point of each random sample automatically with the PCC algorithm, we succeed in studying the sample-dependent $T_c(L)$ and the sample average of physical quantities at each $T_c(L)$ systematically. Using the finite-size scaling (FSS) analysis for $T_c(L)$, we discuss the importance of corrections to FSS both in the strong-dilution and weak-dilution regions. The critical phenomena of the 2D site-diluted Ising model are shown to be controlled by the pure fixed point. The crossover from the percolation fixed point to the pure Ising fixed point with the system size is explicitly demonstrated by the study of the Binder parameter. We also study the distribution of critical temperature $T_c(L)$. Its variance shows the power-law $L$ dependence, $L^{-n}$, and the estimate of the exponent $n$ is consistent with the prediction of Aharony and Harris [Phys. Rev. Lett. {\bf 77}, 3700 (1996)]. Calculating the relative variance of critical magnetization at the sample-dependent $T_c(L)$, we show that the 2D site-diluted Ising model exhibits weak self-averaging.Comment: 6 pages including 6 eps figures, RevTeX, to appear in Phys. Rev.

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 $c$ is calculated from the leading finite-width correction to the averaged free energy on strips. Estimates thus obtained are consistent with $c=1/2$, the same as for the pure Ising model.Comment: RevTeX 3, 11 pages +2 figures, uuencoded, IF/UFF preprin

Critical behavior of weakly-disordered anisotropic systems in two dimensions

The critical behavior of two-dimensional (2D) anisotropic systems with weak quenched disorder described by the so-called generalized Ashkin-Teller model (GATM) is studied. In the critical region this model is shown to be described by a multifermion field theory similar to the Gross-Neveu model with a few independent quartic coupling constants. Renormalization group calculations are used to obtain the temperature dependence near the critical point of some thermodynamic quantities and the large distance behavior of the two-spin correlation function. The equation of state at criticality is also obtained in this framework. We find that random models described by the GATM belong to the same universality class as that of the two-dimensional Ising model. The critical exponent $\nu$ of the correlation length for the 3- and 4-state random-bond Potts models is also calculated in a 3-loop approximation. We show that this exponent is given by an apparently convergent series in $\epsilon=c-\frac{1}{2}$ (with $c$ the central charge of the Potts model) and that the numerical values of $\nu$ are very close to that of the 2D Ising model. This work therefore supports the conjecture (valid only approximately for the 3- and 4-state Potts models) of a superuniversality for the 2D disordered models with discrete symmetries.Comment: REVTeX, 24 pages, to appear in Phys.Rev.

On electrostatic and Casimir force measurements between conducting surfaces in a sphere-plane configuration

We report on measurements of forces acting between two conducting surfaces in a spherical-plane configuration in the 35 nm-1 micrometer separation range. The measurements are obtained by performing electrostatic calibrations followed by a residual analysis after subtracting the electrostatic-dependent component. We find in all runs optimal fitting of the calibrations for exponents smaller than the one predicted by electrostatics for an ideal sphere-plane geometry. We also find that the external bias potential necessary to minimize the electrostatic contribution depends on the sphere-plane distance. In spite of these anomalies, by implementing a parametrixation-dependent subtraction of the electrostatic contribution we have found evidence for short-distance attractive forces of magnitude comparable to the expected Casimir-Lifshitz force. We finally discuss the relevance of our findings in the more general context of Casimir-Lifshitz force measurements, with particular regard to the critical issues of the electrical and geometrical characterization of the involved surfaces.Comment: 22 pages, 15 figure

On Emery-Kivelson line and universality of Wilson ratio of spin anisotropic Kondo model

Yuval-Anderson's scaling analysis and Affleck-Ludwig's Conformal Field Theory approach are applied to the $k$ channel {\em spin anisotropic} Kondo model. Detailed comparisons with the available Emery-Kivelson's Abelian Bosonization approaches are made. It is shown that the EK line exists for any $k$, although it can be mapped to free fermions only when $k=1$ or $2$. The Wilson ratio is universal if $k=1$ or $2$, but {\em not} universal if $k>2$. The leading low temperature correction to the electron resistivity is {\em not} affected by the spin anisotropy for {\em any} $k$. A new universal ratio for $k>2$ is proposed to compare with experiments.Comment: 12 pages, REVTEX, no figures, to appear in Phys. Rev. Lett

A new non-Fermi liquid fixed point

We study a new exchange interaction in which the conduction electrons with pseudo spin $S_c=3/2$ interact with the impurity spin $S_I=1/2$. Due to the overscreening of the impurity spin by higher conduction electron spin, a new non-trivial intermediate coupling strength fixed point is realized. Using the numerical renormalization group (NRG), we show that the low-energy spectra are described by a non-Fermi liquid excitation spectrum. A conformal field theory analysis is compared with NRG results and excellent agreement is obtained. Using the double fusion rule to generate the operator spectrum with the conformal theory, we find that the specific heat coefficient and magnetic susceptibility will diverge as $T^{-2/3}$, that the scaling dimension of an applied magnetic field is $5/6$, and that exchange anisotropy is always relevant. We discuss the possible relevance of our work to two-level system Kondo materials and dilute cerium alloys, and we point out a paradox in understanding the Bethe-Ansatz solutions to the multichannel Kondo model.Comment: Revised. 20 page

Low energy properties of M-state tunneling systems in metals: New candidates for non-Fermi-liquid systems

We construct a generalized multiplicative renormalization group transformation to study the low energy dynamics of a heavy particle tunneling among $M$ different positions and interacting with $N_f$ independent conduction electron channels. Using a $1/N_f$-expansion we show that this M-level scales towards a fixed point equivalent to the $N_f$ channel $SU(M) \times SU(N_f)$ Coqblin-Schrieffer model. Solving numerically the scaling equations we find that a realistic M-level system scales close to this fixed point (FP) and its Kondo temperature is in the experimentally observable range $1-10 K$.Comment: 11 Latex pages, to appear in Phys. Rev. Lett, Figures available from the author by reques