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.

24 pages, 4 figures. The combinatoric derivation of the (unchanged) algorithm is corrected.

References in corpus (6)

• Simulating the All-Order Strong Coupling Expansion I: Ising Model Demo
• Precision check on triviality of phi^4 theory by a new simulation method
• Simulating the All-Order Strong Coupling Expansion III: O(N) sigma/loop models
• Critical Loop Gases and the Worm Algorithm
• Efficient Cluster Algorithm for CP(N-1) Models
• An Efficient Cluster Algorithm for CP(N-1) Models

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