FINITE SIZE SCALING AND RUNNING COUPLING CONSTANT IN CPN-1 MODELS

Abstract

In this work I present a numerical study of the Finite Size Scaling (FSS) of a correlation length in the framework of the CPN-1 model by means of the 1/N expansion. This study has been thought as preparatory to the application of FSS to the measure on the lattice of a new coupling constant fx(1/R), defined in terms or rectangular Wilson loops. I give also a perturbative expansion of fx(1/R) in powers of the corresponding coupling constant in the [Formula: see text] scheme together with some preliminary numerical results obtained from the Polyakov ratio and I point out the conceptual problems that limit this approach.