Critical Loop Gases and the Worm Algorithm

Abstract

The loop gas approach to lattice field theory provides an alternative, geometrical description in terms of fluctuating loops. Statistical ensembles of random loops can be efficiently generated by Monte Carlo simulations using the worm update algorithm. In this paper, concepts from percolation theory and the theory of self-avoiding random walks are used to describe estimators of physical observables that utilize the nature of the worm algorithm. The fractal structure of the random loops as well as their scaling properties are studied. To support this approach, the O(1) loop model, or high-temperature series expansion of the Ising model, is simulated on a honeycomb lattice, with its known exact results providing valuable benchmarks.

34 pages, 12 figures; v2: 2 figures and 1 table added; v3: typo's corrected

References in corpus (1)

• Simulating the All-Order Strong Coupling Expansion I: Ising Model Demo

Cited by in corpus (7)

• Simulating the All-Order Strong Coupling Expansion IV: CP(N-1) as a loop model
• Worm Monte Carlo study of the honeycomb-lattice loop model
• The worm process for the Ising model is rapidly mixing
• Geometric allocation approach to accelerating directed worm algorithm
• Lifted directed-worm algorithm
• Statistical properties of worm algorithms for two dimensional frustrated Ising models
• Critical Line of the O($N$) Loop Model on the Square Lattice