Simulating the All-Order Strong Coupling Expansion IV: CP(N-1) as a loop model

TL;DR

This paper reformulates the lattice CP(N-1) spin model as a loop model, enabling efficient Monte Carlo sampling that avoids critical slowing down and confirms universality across different lattice actions.

Contribution

It introduces an exact loop model reformulation of the CP(N-1) spin system and develops a Monte Carlo algorithm that efficiently samples configurations without critical slowing down.

Findings

No critical slowing down observed at D=2

Monte Carlo algorithm successfully samples loop configurations

Universality demonstrated via finite size scaling

Abstract

We exactly reformulate the lattice CP(N-1) spin model on a D dimensional torus as a loop model whose configurations correspond to the complete set of strong coupling graphs of the original system. A Monte Carlo algorithm is described and tested that samples the loop model with its configurations stored and manipulated as a linked list. Complete absence of critical slowing down and correspondingly small errors are found at D=2 for several observables including the mass gap. Using two different standard lattice actions universality is demonstrated in a finite size scaling study. The topological charge is identified in the loop model but not yet investigated numerically.