Critical behavior of classical spin models and local cohomology

Abstract

Using reflection positivity as the main tool, we establish a connection between the existence of a critical point in classical spin models and the triviality of a certain local cohomology class related to the Noether current of the model in the continuum limit. Furthermore we find a relation between the location of the critical point and the momentum space autocorrelation function of the Noether current.

Comments: 13 pages, Talk given at the XIIth Max Born Symposioum, Wroclaw, Poland. Some misprints corrected