Ornstein-zernike and analyticity properties for classical lattice spin systems

ANNALS

OF PHYSICS

115,

Abstracts

On the Theory

248-249 (1978)

of Papers

of Vibration-Rotation

of Theoretical

to

Appear

Interaction.

NANNY

in Future

FR~MAN

AND

Issues

PER OLOF FR~MAN, Institute

Physics, University of Uppsala, Uppsala, Sweden.

In a paper published by Langer in 1949 it was shown that the eigenvalues X of a rotating harmonic oscillator, containing a parameter oi < 1, are given by the formula X = v + O(a In cc),where v is an integer. In the present paper it is shown that Langer’s estimate is too rough; the correct formula is h = v + I(1 + 1)~ + higher powers of N. Ornstein-Zernike LEME,

and Analyticity

Properties

for

Classical

Lattice

Spin Systems.

PAULO

JORGE

PAES-

The Rockefeller University, New York, New York 10021.

The leading Ornstein-Zernike behavior of the truncated two-point function G(x) is obtained from information on the poles of the Fourier transform G”(p). Analyticity of G”(p) as a function of the complex variables p and the inverse temperature /J is studied in detail for I b 1 sufficiently small.

Classically

Solvable

Field

Theory

Model.

FERNANDO

LUND, The Institute for Advanced Study, Olde

Lane, Princeton, New Jersey 08540. The embedding of a surface in a three-dimensional Euclidean space provides a natural way of associating a linear problem with a nonlinear evolution equation. This fact is here exploited to solve a particular set of coupled Lorentz-invariant equations arising in a number of different contexts. Light-cone coordinates are used for simplicity in the inverse scattering method. The system has soliton solutions and an infinite set of polynomial conserved quantities. Sine-Gordon theory is a particular case of the problem considered. Crossover AND

of the

Behavior YADIN

Y.

Jerusalem, Israel Rome, Italy.

Nonlinear

u-Model

Broken Symmetry. DANIEL J. AMIT of Physics, Hebrew University of Jerusalem, Fisica and G.N.S.M.-CNR, Unita di Roma,

with Quadratically

GOLDSCHMIDT, Racah Institute AND LUCA PELITI, Istituto di

We study the nonlinear o-model near two dimensions in the presence of a quadratic symmetry breaking, which gives a mass to M of the N fields. Using a renormalization scheme, proposed earlier, which includes the anisotropy mass explicitly, and making sure that the renormalized mass is a physical parameter, we calculate explicitly, to first order in d - 2; the flow patterns of the temperature (coupling constant); the crossover in temperature and external magnetic field of the order-parameter (the average classical field); and the crossover in momentum of the two-point Green function. The Equivalence

of Technology,

Theorem

Kanpur

Is Subtle.

H.

S. SHARATCHANDRA,

Physics Department,

Indian Institute

208016, India.

We show that the equivalence theorem as is usually stated is valid only within the scheme of perturbation theory. New conditions have to be imposed on the theorem to make it valid in a nonperturbative context. Implications for a nonperturbative quantization of gravitation as also quantization of gauge theories in the unitary gauge are discussed.

248 0003-4916/78/1151-0248$05.00/0 Copyright AI1 rights

0 1978 by Academic Press, Inc. of reproduction in any form reserved.