  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.
