Finite Size Scaling and Running Coupling Constant in CP(N-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 $C{P}^{N-1}$ model by means of the 1/N expansion. This study has been thought as propedeutical to the application of FSS to the measure on the lattice of a new coupling constant $f_x(1/R)$, defined in terms or rectangular Wilson Loops. I give also a perturbative expansion of $f_x(1/R)$ in powers of the corresponding coupling constant in the $\overline{MS}$ scheme together with some preliminary numerical results obtained from the Polyakov ratio and I point out the conceptual problems that limit this approach.

17 pages in REVTex + 6 figures, to be published in International Journal of Modern Physics A

References in corpus (1)

• Running coupling constant and correlation length from Wilson loops