Finite size effects and scaling in lattice CP(N-1)

TL;DR

This paper investigates finite size effects in lattice $CP^{N-1}$ models, providing predictions for the spectrum and analyzing how different lattice actions and algorithms influence scaling and efficiency.

Contribution

It offers new model predictions for the spectrum of $CP^{N-1}$ in finite volumes and discusses the impact of lattice actions and algorithms on finite size effects and scaling behavior.

Findings

Finite size effects are significant in lattice $CP^{N-1}$ models.

Asymptotic scaling behavior varies with different lattice actions.

Multigrid algorithms' efficiency is analyzed in this context.

Abstract

We present model predictions for the spectrum of $CP^{N-1}$ in a periodic box and use them to interpret the strong finite size effects observed in lattice simulations at medium values of $N$. The asymptotic scaling behaviour of alternative lattice actions is discussed along with some aspects of multigrid algorithm efficiency.