Critical Loop Gases and the Worm Algorithm

Details Critical Loop Gases and the Worm Algorithm Critical Loop Gases and the Worm Algorithm

2009-10-27

arxiv.org/abs/0910.5231v3

Nucl. Phys. B829:573-599,2010

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1016/j.nuclphysb.2009.12.024

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.

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