In this paper we find non-trivial vacuum states for the renormalizable non-commutative φ4 model. An associated linear sigma model is then considered. We further investigate the corresponding spontaneous symmetry breaking.
Marcillaud de Goursac, A., Tanasa, A., & Wallet, C. (2008). Vacuum configurations for renormalizable non-commutative scalar models. European Physical Journal C. Particles and Fields, 53, 459-466. https://doi.org/10.1140/epjc/s10052-007-0465-6 (Original work published 2008)