Su(2) Chiral Model in an External Field: A Complex Stochastic Process on a Non-Abelian Group

摘要

The principal chiral model in an external field has a complex action. Conventional methods for performing Monte Carlo simulations are therefore useless for strong fields or weak coupling (i.e. large lattices). We apply the Langevin equation to this action and generate a complex stochastic process on a non-abelian group. Nice agreement with the perturbative expansion is observed for strong fields. A clear verification of the second order phase transition for weak fields proved by Polyakov and Wiegmann seems to require larger lattices and more computer time than we have available, but should be straightforward using the complex Langevin equation. (ERA citation 11:057577)