Scaling limits in statistical mechanics and microstructures in continuum mechanics
Presutti, E.
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. Thebook 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, calculusof variations and PDE are discussed at length. INDICE: Introduction.- Thermodynamic limit in the Ising model.- The phase diagram of Ising systems.- Mean field, Kac potentials and the Lebowitz-Penroselimit.- 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.- Phasetransitions in the LMP model.- DLR measures and the ergodic decomposition.- Appendix A: Ising model.- Appendix B: Geometric measure theory.- References.- Index.
- ISBN: 978-3-540-73304-1
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 510
- Fecha Publicación: 01/10/2008
- Nº Volúmenes: 1
- Idioma: Inglés