Infinite-order phase transition in a classical spin system

For an exactly soluble classical spin model with long-range inhomogeneous coupling it is proved that in the absence of external magnetic field the free energy is aC function of the temperature at the critical point.     

An extended continuous Newton method

This paper describes a numerical realization of an extended continuous Newton method defined by Diener. It traces a connected set of locally one-dimensional trajectories which contains all critical points of a smooth functionf: ⁿ . The results show that the method is effectively applicable.The authors would like to thank L. C. W. Dixon for pointing out some errors in the original version of this paper and for several suggestions of improvements.     

Two-dimensional exponential model of the Euclidean field theory

It is proved that the two-dimensional exponential model of the field theory is trivial for ² > 8.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 469–477, April, 1990.     

Ray Theory of the Diffraction of Sound by an Inhomogeneous Membrane

Present address: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, U.K. In this paper, a ray approach is developed for calculating theacoustic radiation into a fluid generated by a localized forcingon an elastic boundary. We consider here the case of fluid-loadedmembrane with a rigid line-mass distribution subject to infiniteplane-wave incidence from the fluid. It is demonstrated howray methods can be used to determine each of the constituentwaves of the scattered acoustic field, showing that non-uniformitiesarise whenever two such waves have tangential wavefronts. Transitionanalyses are presented to remove these non-uniformities, resultingin the prediction of beam-like structures in the scattered field.     

Vibrotactile temporal gap detection as a function of age

The ability of subjects to detect temporal gaps between bursts of sinusoids or bursts of bandlimited noise was measured to evaluate the phenomenon of tactile "sensory persistence" in older persons. Vibratory stimuli were delivered to the right thenar eminence of 27 subjects ranging in age from 8-75 years. The subjects' task was to detect the presence of a silent interval or "gap" between flanking 350-ms vibrotactile stimuli. The gap-detection threshold, expressed as the amplitude of vibration relative to the absolute detection threshold, decreased as the gap duration increased and was higher for gaps in noise than for gaps in sinusoids. The threshold for detecting short gaps increased with age for noise stimuli, but not for sinusoidal stimuli. Furthermore, the gap-detection threshold recovered more rapidly in older subjects for noise stimuli, but less rapidly in older subjects for sinusoidal stimuli. Because of these differences, it appears that the effects of age on gap detection cannot be due to a simple increase in sensory persistence, but may be due to multiple processes.     

A numerical analysis of chaotic behaviour in Bianchi IX models

In this paper we investigate the chaotic behaviour of the Bianchi IX cosmological models using techniques developed in the study of dynamical systems and chaotic behaviour. We numerically calculate the Lyapunov exponent, , and show that instead of converging to a constant value, it decreases steadily. We study this effect further by studying the Lyapunov exponent using short-time averages. We show that the usual method of calculating is invalid in the case of a cosmological model.     

Hamiltonian limit of the 3D Zamolodchikov model

A two-dimensional quantum Hamiltonian _N,M commuting with the layer-to-layer transfer matrix of the three-dimensional Zamolodchikov model is derived. This Hamiltonian is defined on a lattice ofN×M sites. The special casesN×2, 2×M, and 3×M are studied.This paper is dedicated to Cyril Domb.     

SO(n,1) Wigner rotation as an SL(2,R) problem

We show that the composition of not only two SO(3,1) boosts, but also that of two SO(n,1) boosts for anyn 2, is basically an SO(2,1) problem and hence can be analysed completely using SL(2,R) matrices. By computing the expression for the Thomas/Wigner angle directly using SL(2,R) matrices we show that this approach results in considerable economy of algebra.     

Random fields and quantum effects in proton glasses

The effects of quantum fluctuations on the proton glass phase in mixed hydrogen-bonded ferro-antiferroelectric systems are considered. The system is described in terms of the infinite-ranged Ising pseudospin glass model in a transverse tunneling field in the presence of random parallel fields. The stability limit of the high-temperature proton glass phase is determined within the thermofield dynamic approach, and the behavior or linear and nonlinear susceptibility is evaluated.     

Electronic surface states on Pd(110): Theory and comparison with experiment

A relativistic Green function formalism has been applied to calculate layer-projected densities of states on Pd(110). In particular, we obtained unoccupied surface states and their dispersion relations along two directions in the surface Brillouin zone. Good agreement with recent inverse photoemission data is reached by using an energy-dependent dynamical surface potential barrier, which is based on a simple electron-plasmon interaction model, instead of a static surface barrier.