Simulating the All-Order Strong Coupling Expansion III: O(N) sigma/loop models

Abstract

We reformulate the O(N) sigma model as a loop model whose configurations are the all-order strong coupling graphs of the original model. The loop configurations are represented by a pointer list in the computer and a Monte Carlo update scheme is proposed. Sample simulations are reported and the method turns out to be similarly efficient as the reflection cluster method, but it has greater potential for systematic generalization to other lattice field theories. A variant action suggested by the method is also simulated and leads to a rather extreme demonstration of the concept of universality of the scaling or continuum limit.

27 pages, 6 figures, 5 tables. The combinatoric derivation of the (unchanged) algorithm is corrected. Independently, all data in sect.5 are revised due to a software error, with unchanged conclusions on universality.