Simulating the all-order strong coupling expansion IV: CP(N−1) as a loop model

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.

Simulating QCD at finite density

“…Its limits of applicability are not clear yet. It appears to work well for at least one model, the 2d CP N−1 spin model [78], where cluster algorithms are known to fail. If the random worms can be generalized to random surfaces, then one could apply the same treatment to the Yang-Mills part of the action and simulate QCD at weak coupling, as a gas of quark loops forming the boundary of gauge surfaces.…”

Fighting topological freezing in the two-dimensional CPN−1 model

“…These can be simulated by using the worm algorithm [18,19]. In these dual formulations there are no topological sectors and hence severe slowing down does not occur in the simulation.…”

Phase transitions in three-dimensional loop models and theCPn−1sigma model

“…The 2D CP n−1 sigma model has been simulated both by using the connection between SU (n) magnets in (1 + 1) dimensions and classical σ models in 2 dimensions, 15 and by means of a loop representation different from the one we describe here. 16 Separately, there have been detailed studies of the properties of loops that arise in the description of some frustrated classical antiferromagnets, 17,18 and of cycles that occur in statistical problems involving random permutations.…”