CRITICAL EXPONENTS IN THE SINGLE-PARAMETER HIGHEST CATASTROPHE-THEORY

On the basis of elementary catastrophe theory a direct calculation of the critical exponents of systems described by a one-component order p arameter is performed. It is shown that in the approximation, which is a version of a self-consistent field method, critical exponents can d iffer from classical values corresponding to the Landau theory. The sc heme proposed allows one to get results satisfying the universal Rushb rooke-Griffiths-Fisher-Widom relations connecting the critical exponen ts which appear to be dependent on natural parameters of the correspon ding Landau potential and allows one to obtain strictly determined dis crete values. The Ginzburg-Levanyuk criterion, determining the applica tion range of the small fluctuating approximation, in the approach dev eloped here is discussed. In order to account for critical fluctuation s, the scale-invariant effective potential, which is analogous to a ca tastrophe function, is introduced.