These notes contain material related to the five lectures that I have delivered at the University of Utah in the week 16--20 May 2005. They are organized in the order of the lectures; namely,

1. Spin systems. An introduction to lattice systems

2. Limits of finite-difference lattice systems.

3. Bounds for linear networks.

4. A model for a membrane with randomly-distributed defects.

5. Derivation of fracture energies from inter-atomic potentials.
 

The notes are thought just as a complement and reference for the single lectures, and not as a whole: I must warn that the chapters are unevenly written. Some are elaboration of articles that have already appeared and some have been completely written for the occasion. As a consequence some notation may slightly vary from chapter to chapter.
 
 
 

Related links:
Gamma-convergence for beginners - notes of a PhD course
Course on limits of one-dimensional discrete systems
 
 
 

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