Scaling and asymptotic scaling in two-dimensional $CP^{N-1}$ models

TL;DR

This study uses Monte Carlo simulations to analyze scaling behaviors in two-dimensional $CP^{N-1}$ models across various N values, revealing how different lattice formulations and coupling constants affect scaling and finite size effects.

Contribution

It demonstrates that multiple lattice formulations exhibit scaling at small correlation lengths and shows that using $eta_E$ improves asymptotic scaling, highlighting complex finite size effects at large N.

Findings

Scaling observed for $\xi$ as small as 2.5 across formulations

Using $eta_E$ enhances asymptotic scaling properties

Finite size effects depend strongly on N due to bound state radius growth

Abstract

Two-dimensional $CP^{N-1}$ models are investigated by Monte Carlo methods on the lattice, for values of $N$ ranging from 2 to 21. Scaling and rotation invariance are studied by comparing different definitions of correlation length $\xi$. Several lattice formulations are compared and shown to enjoy scaling for $\xi$ as small as $2.5$. Asymptotic scaling is investigated using as bare coupling constant both the usual $\beta$ and $\beta_E$ (related to the internal energy); the latter is shown to improve asymptotic scaling properties. Studies of finite size effects show their $N$-dependence to be highly non-trivial, due to the increasing radius of the $\bar z z$ bound states at large $N$.