The pivot algorithm and polygons: results on the FCC lattice

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Abstract
The authors consider the pivot algorithm for polygons on the face-centred cubic lattice and prove ergodicity. A numerical study of the algorithm is carried out; in particular, the authors look at the acceptance fraction of the elementary moves and find that it goes only slowly to zero as the length of the polygons is increased. The numerical properties of polygons on the FCC lattice are also considered. They calculate the exponent nu (by considering the mean square radius of gyration of the polygons) and compare the result to the expected value (from field theory). They also consider the mean span of the polygons and discuss corrections to scaling and their influence on the numerical calculation of critical exponents.