Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics

• Main Author: Presutti, Errico (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Theoretical and Mathematical Physics,
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Physics.; Dynamical Systems and Ergodic Theory.; Mathematical Methods in Physics.

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:

• Statistical Mechanics of Ising systems
• Thermodynamic limit in the Ising model
• The phase diagram of Ising systems
• Mean field, Kac potentials and the Lebowitz–Penrose limit
• Stochastic Dynamics
• Mesoscopic Theory, non-local functionals
• Non-local, free energy functionals
• Surface tension, Gamma convergence, Wulff shape
• One dimensional interfaces
• Phase transitions in systems with Kac potentials
• 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.