Sämann, Christian The multitrace matrix model of scalar field theory on fuzzy \(\mathbb {C}P^n\). (English) Zbl 1217.81140 SIGMA, Symmetry Integrability Geom. Methods Appl. 6, Paper 050, 23 p. (2010). Summary: We perform a high-temperature expansion of scalar quantum field theory on fuzzy \(\mathbb {C}P^n\) to third order in the inverse temperature. Using group theoretical methods, we rewrite the result as a multitrace matrix model. The partition function of this matrix model is evaluated via the saddle point method and the phase diagram is analyzed for various \(n\). Our results confirm the findings of a previous numerical study of this phase diagram for \(\mathbb {C}P^n\). Cited in 7 Documents MSC: 81T75 Noncommutative geometry methods in quantum field theory 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81T28 Thermal quantum field theory 82B30 Statistical thermodynamics Keywords:matrix models; fuzzy geometry PDFBibTeX XMLCite \textit{C. Sämann}, SIGMA, Symmetry Integrability Geom. Methods Appl. 6, Paper 050, 23 p. (2010; Zbl 1217.81140) Full Text: DOI arXiv EuDML