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Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics (Theoretical and Mathematical Physics)by Errico Presutti
Synopses & Reviews
Collective behavior in systems with many components, blow-ups with emergence of microstructures are proofs of the double, continuum and atomistic, nature of macroscopic systems, an issue which has always intrigued scientists and philosophers. Modern technologies have made the question more actual and concrete with recent, remarkable progresses also from a mathematical point of view. The book focuses on the links connecting statistical and continuum mechanics and, starting from elementary introductions to both theories, it leads to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length.
Focusing on the links connecting statistical and continuum mechanics, this book introduces both theories before leading on to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length.
About the Author
Errico Presutti is professor of classical mechanics at the Department of Mathematics of the University of Roma Tor Vergata.
Table of Contents
Introduction.- Thermodynamic limit in the Ising model.- The phase diagram of Ising systems.- Mean field, Kac potentials and the Lebowitz-Penrose limit.- Stochastic dynamics.- Non local, free energy functional.- Surface tension, Gamma convergence, Wulff shape.- One dimensional interfaces.- Ising systems with Kac potentials.- The LMP model and the Pirogov-Sinai strategy.- Phase transitions in the LMP model.- DLR measures and the ergodic decomposition.- Appendix A: Ising model.- Appendix B: Geometric measure theory.- References.- Index.
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