Chiral orders in the two-dimensional Heisenberg model

Abstract

It is proved using Bogoliubov's inequality that no vector chiral order appears at finite temperatures in the two-dimensional antiferromagnetic Heisenberg model with short-range interaction. The proof can be extended and is applicable to a wide class of order parameters. Scalar chiral orders in the Heisenberg model with frustration are also investigated using the super-effective field theory. The numerical results show that correlations between local chiral orders are weak. This suggests that no chiral phase transition takes place in this case.