Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics

• Main Author: Presutti, Errico. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Theoretical and Mathematical Physics,
• Subjects: Mathematics.; Differentiable dynamical systems.; Mathematical physics.; Dynamical Systems and Ergodic Theory.; Mathematical Methods in Physics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-540-73305-8

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 an...

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.