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

Critical Loop Gases and the Worm Algorithm