Detecting scaling in phase transitions on the truncated Heisenberg algebra

Abstract

We construct and analyze a phase diagram of a self-interacting matrix field coupled to curvature of the non-commutative truncated Heisenberg space. The model reduces to the renormalizable Grosse-Wulkenhaar model in an infinite matrix size limit and exhibits a purely non-commutative non-uniformly ordered phase. Particular attention is given to scaling of model's parameters. We additionally provide the infinite matrix size limit for the disordered to ordered phase transition line.

v2: Paper restructured. New data and additional section added. Some notation changed. Major revision. v3: Typos from convention change corrected. Three figures added, one removed. Minor text changes