A04 – Statistical mechanics for lattice models of elasticity
The long term goal of this project is an understanding of the statistical mechanics of nonlinearly elastic materials. Of course, in the strict sense elasticity is not an equilibrium phenomenon, but only a metastable one. Indeed no material can withstand shear on an infinitely long time scale since processes like the rearrangement of atoms can relax any applied shear. In practice, however, elasticity persists even on geological time scales. To rule out complete reordering we will focus here on models where the local neighbourhood relations are fixed (see [BLM06], [LM10] for models which to some extent remove this restriction). The main tool is a rigorous renormalization group approach in the spirit of Brydges and Yau. We will use this to study strict convexity properties of the free energy, correlation functions and possible phase transitions.