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Author:   Errico Presutti
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2009 ed.
Dimensions:   Width: 15.50cm , Height: 2.60cm , Length: 23.50cm
Weight:   0.893kg
ISBN:  

9783540733041

ISBN 10:   3540733043
Pages:   470
Publication Date:   15 October 2008
Audience:   Professional and scholarly ,  College/higher education ,  Professional & Vocational ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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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.

Reviews

From the reviews: The author takes an effort to make accessible a variety of problems and mathematical techniques involved in describing how a continuum description emerges from mesoscopic and microscopic models. Technically that refers to large scale phenomena in statistical mechanics and their mathematical formulations in terms of thermodynamic and hydrodynamic limits. The book is intended to both (mathematical) physics and mathematical communities ! . (Piotr Garbaczewski, Zentralblatt MATH, Vol. 1156, 2009) This book is a beautiful overview of the state of the art. ! The link between notions and theories developed in continuum mechanics and PDEs and statistical mechanics is illustrated here. The book is an effort to build bridges between the two areas and, since it is meant for both communities it is written with the presumption that reader may not be expert in all topics. ! The various topics can be easily singled out to be used for courses or lectures ! . (Nicoletta Cancrini, Mathematical Reviews, Issue 2011 a)

From the reviews: The author takes an effort to make accessible a variety of problems and mathematical techniques involved in describing how a continuum description emerges from mesoscopic and microscopic models. Technically that refers to large scale phenomena in statistical mechanics and their mathematical formulations in terms of thermodynamic and hydrodynamic limits. The book is intended to both (mathematical) physics and mathematical communities ! . (Piotr Garbaczewski, Zentralblatt MATH, Vol. 1156, 2009)

Author Information

Errico Presutti is professor of classical mechanics at the Department of Mathematics of the University of Roma Tor Vergata.

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