Abstract
We derive the Wulff construction for Kac-Ising models with long but finite range interaction in dimensions d >/ 2. Some open problems concerning the phase coexistence for more general models are also discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
K. Alexander, Cube-root boundary fluctuations for droplets in random cluster models, preprint (2000).
G. Alberti and G. Bellettini, Asymptotic behavior of a non local anisotropic model for phase transition, J. Math. Ann. 310, No. 3 (1998), 527–560.
G. Alberti, G. Bellettini, M. Cassandro, and E. Presutti, Surface tension in Ising system with Kac potentials, J. Stat. Phys.82 (1996), 743–796.
K. Alexander, J.T. Chayes, and L. Chayes, The Wulff construction and asymptotics of the finite cluster distribution for the two-dimensional Bernoulli percolation, Comm. Math. Phys. 131 (1990), 1–50.
G. Bellettini, M. Cassandro, and E. Presutti, Constrained minima of non local free energy functionals, J. Stat. Phys.84 (1996), 1337–1349.
O. Benois, T. Bodineau, P. Butta, and E. Presutti, On the validity of van der Waals theory of surface tension, Mark. Proc. andRel. Fields 3(1997), 175–198.
O. Benois, T. Bodineau, and E. Presutti, Large deviations in the van der Waals limit, Stoch. Proc. andAppl. 75 (1998), 89–104.
T. Bodineau, The Wulff construction in three and more dimensions, Comm. Math. Phys. 207 (1999), 197–229.
T. Bodineau, A microscopic derivation of 3D equilibrium crystal shapes,ICMP Proceedings (2000).
T. Bodineau, D. Ioffe, and Y. Velenik, Rigorous probabilistic analysis of equilibrium crystal shapes,J. Math. Phys. 41, No.3 (2000), 1033–1098.
T. Bodineau, D. Ioffe, and Y. Velenik, Winterbottom construction for finite range ferromagnetic models: a L 1-approach, preprint (2000).
A. Bovier and M. Zahradnik, The low-temperature phase of Kac-Ising models,J. Stat. Phys. 87, No.1–2 (1997), 311–332.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Bodineau, T. (2002). Phase Coexistence for the Kac-Ising Models. In: Sidoravicius, V. (eds) In and Out of Equilibrium. Progress in Probability, vol 51. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0063-5_3
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0063-5_3
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6595-5
Online ISBN: 978-1-4612-0063-5
eBook Packages: Springer Book Archive