Nonlinear sigma models (A08)

• Subject Area: Mathematics
• Term: since 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 211504053

Simple statistical mechanics models on a lattice, such as the Ising or the XY-model, are oversimplified descriptions of reality but are key ingredients in the study of phase transitions and critical phenomena, since they arise as the effective description of a large variety of models. It is therefore important to enlarge the class of well-understood models. This project focuses on nonlinear sigma models, in particular O(n) models and certain generalizations. Applications include quantum diffusion in disordered materials as well as the emergence of unusual anisotropic orderings, such as nematic order in liquid cristals.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1060: The Mathematics of Emergent Effects
• Applicant Institution: Rheinische Friedrich-Wilhelms-Universität Bonn
• Project Head: Professorin Dr. Margherita Disertori