English

Critical Loop Gases and the Worm Algorithm

Statistical Mechanics 2010-02-10 v3 High Energy Physics - Lattice

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.

Keywords

Cite

@article{arxiv.0910.5231,
  title  = {Critical Loop Gases and the Worm Algorithm},
  author = {Wolfhard Janke and Thomas Neuhaus and Adriaan M. J. Schakel},
  journal= {arXiv preprint arXiv:0910.5231},
  year   = {2010}
}

Comments

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

R2 v1 2026-06-21T14:04:03.869Z