Finite size scaling in CP(N-1) models

TL;DR

This paper investigates finite size effects in Euclidean CP(N-1) models using analytical and numerical methods, comparing results for various physical quantities and explaining discrepancies at large volumes.

Contribution

It provides a combined analytical and numerical study of finite size effects in CP(N-1) models, including new insights into bound state effects and topological quantities.

Findings

Analytic and numerical results agree for small volumes.

Discrepancies at large volumes explained by bound state extension.

Finite size effects on string tension match simulations.

Abstract

Finite size effects in Euclidean ${\rm CP}^{N-1}$ models with periodic boundary conditions are investigated by means of the $1/N$ expansion and by Monte Carlo simulations. Analytic and numerical results for magnetic susceptibility and correlation length are compared and found to agree for small volumes. For large volumes a discrepancy is found and explained as an effect of the physical bound state extension. The leading order finite size effects on the Abelian string tension are computed and compared with simulations finding agreement. Finite size dependence of topological quantities is also discussed.