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Towards a Microscopic Theory of Phase Coexistence

  • Conference paper
European Congress of Mathematics

Part of the book series: Progress in Mathematics ((PM,volume 202))

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Abstract

One of the fundamental goals of statistical mechanics is to understand the macroscopic effects induced by random forces acting at the microscopic level. We illustrate this in the context of the Ising model in the phase coexistence regime: the most likely shapes of macroscopic droplets of one pure phase floating in the other pure phase are close to the Wulff crystal of the model. Furthermore, the law of configurations at equilibrium is governed by a minimal action principle. These results come from joint works with Agoston Pisztora. We list several related open problems.

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Author information

Authors and Affiliations

  1. Université Paris Sud Mathématique, Bâtiment 425, Orsay Cedex, 91405, France

    Raphaël Cerf

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  1. Raphaël Cerf
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Editor information

Editors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    Carles Casacuberta  & Joan Verdera  & 

  2. Departament d’Algebra i Geometria Facultat de Matemàtiques, Universitat de Barcelona, 08007, Barcelona, Spain

    Rosa Maria Miró-Roig

  3. Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, 08028, Barcelona, Spain

    Sebastià Xambó-Descamps

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© 2001 Springer Basel AG

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Cerf, R. (2001). Towards a Microscopic Theory of Phase Coexistence. In: Casacuberta, C., Miró-Roig, R.M., Verdera, J., Xambó-Descamps, S. (eds) European Congress of Mathematics. Progress in Mathematics, vol 202. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8266-8_2

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  • DOI: https://doi.org/10.1007/978-3-0348-8266-8_2

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9496-8

  • Online ISBN: 978-3-0348-8266-8

  • eBook Packages: Springer Book Archive

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