Finite Size Scaling and Running Coupling Constant in CP(N-1) models

TL;DR

This paper investigates the finite size scaling of correlation lengths in CP(N-1) models using 1/N expansion, aiming to measure a new coupling constant via lattice Wilson loops and discussing related perturbative and numerical challenges.

Contribution

It introduces a numerical study of finite size scaling in CP(N-1) models and explores the measurement of a new coupling constant through lattice Wilson loops with perturbative analysis.

Findings

Preliminary numerical results from Polyakov ratio

Perturbative expansion of the new coupling constant

Discussion of conceptual limitations in the approach

Abstract

In this work I present a numerical study of the Finite Size Scaling (FSS) of a correlation length in the framework of the $CP ^{N-1}$ 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.