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Isoperimetric phase transitions of two-dimensional droplets

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Abstract

We consider two-dimensional assemblies of particles governed by hamiltonians depending on the area and the perimeter of their convex hull. Provided the hamiltonian is quadratically homogeneous in the coordinates, we find an exact formula for the free energy. Phase transitions resulting from the competition between area and perimeter can easily be produced and explicitly dealt with. We illustrate those features by a simple example undergoing a second-order transition.

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References

  1. Osserman, R.: Bull. A. M. S.84, 1182–1238 (1978)

    Google Scholar 

  2. Osserman, R.: Am. Math. Monthly86, 1–29 (1979)

    Google Scholar 

  3. Bavaud, F.: J. Stat. Phys.57, 1059–1068 (1989)

    Google Scholar 

  4. Bavaud, F.: Lett. Math. Phys.20, 75–84 (1990)

    Google Scholar 

  5. Zia, R. K. P.: In: Proc. of the XXVIth Scottish Summer School in Physics 1984

  6. Rottman, C., Wortis, M.: Phys. Reports103, 59–79 (1984)

    Google Scholar 

  7. Coninck, J. De., Dunlop, F., Rivasseau, V.: Commun. Math. Phys.121, 401–419 (1989)

    Google Scholar 

  8. Pfister, C. E., Penrose, O.: Commun. Math. Phys.115, 691–699 (1988)

    Google Scholar 

  9. Shlosman, S. B.: Commun. Math. Phys.125, 81–90 (1989)

    Google Scholar 

  10. Santaló, L. A.: Integral Geometry and Geometric Probability. Reading, MA: Addison-Wesley 1976

    Google Scholar 

  11. Baddeley, A.: Adv. Appl. Prob.9, 824–860 (1977)

    Google Scholar 

  12. Dupain, Y., Kamae, T., Mendès-France, M.: Arch. Rat. Mech. Anal.94, 155–166 (1986)

    Google Scholar 

  13. Rényi, A., Sulanke, R.: Z. Wahrscheinlichkeitstheorie3, 138–147 (1964)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Heriot-Watt University, EH14 4AS, Edinburgh, Scotland

    François Bavaud

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  1. François Bavaud
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Communicated by J. Fröhlich

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Bavaud, F. Isoperimetric phase transitions of two-dimensional droplets. Commun.Math. Phys. 132, 549–554 (1990). https://doi.org/10.1007/BF02156536

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  • DOI: https://doi.org/10.1007/BF02156536

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