Monte Carlo simulation of lattice ${\rm CP}^{N-1}$ models at large N

TL;DR

This paper uses Monte Carlo simulations to test large-N predictions of two-dimensional lattice CP(N-1) models, confirming some aspects while revealing slow convergence for others, and employs Simulated Tempering to address critical slowing down.

Contribution

It provides numerical validation of large-N predictions for certain observables in CP(N-1) models at large N, and introduces the use of Simulated Tempering to mitigate critical slowing down.

Findings

Agreement with large-N predictions for correlation length, topological susceptibility, and string tension.

Slow approach to large-N results for the mass gap.

Effective use of Simulated Tempering to reduce critical slowing down.

Abstract

In order to check the validity and the range of applicability of the 1/N expansion, we performed numerical simulations of the two-dimensional lattice CP(N-1) models at large N, in particular we considered the CP(20) and the CP(40) models. Quantitative agreement with the large-N predictions is found for the correlation length defined by the second moment of the correlation function, the topological susceptibility and the string tension. On the other hand, quantities involving the mass gap are still far from the large-$N$ results showing a very slow approach to the asymptotic regime. To overcome the problems coming from the severe form of critical slowing down observed at large N in the measurement of the topological susceptibility by using standard local algorithms, we performed our simulations implementing the Simulated Tempering method.