On the statistical mechanics for non-linear elasticity

Recently there has been some interest in the deduction of the variational principles of non-linear elasticity from statistical mechanics. A powerful tool that is relevant in such derivation is the so-called renormalization group technique. In order to simplify the renormalization group technique a decomposition of the field is needed: the so-called Finite Range Decomposition. In this talk I will discuss how to deduce the finite range decomposition for the non translation invariant case and show haw this may be employed to prove the strict convexity of the free energy near the origin. If time permits, I will also discuss a general representation formula for the free energy.