An Ordered Phase with Slow Decay of Correlations in Continuum $1/r^2$ Ising Models

Fontes, Luiz Renato G.

Ann. Probab., Tome 21 (1993) no. 4, p. 1394-1412 / Harvested from Project Euclid

Résumé

For continuum $1/r^2$ Ising models, we prove that the critical value of the long range coupling constant (inverse temperature), above which an ordered phase occurs (for strong short range cutoff), is exactly 1. This leads to a proof of the existence of an ordered phase with slow decay of correlations. Our arguments involve comparisons between continuum and discrete Ising models, including (quenched and annealed) site diluted models, which may be of independent interest.

Publié le : 1993-07-14
Classification: Ising model, intermediate phase, 60K35

@article{1176989123,
     author = {Fontes, Luiz Renato G.},
     title = {An Ordered Phase with Slow Decay of Correlations in Continuum $1/r^2$ Ising Models},
     journal = {Ann. Probab.},
     volume = {21},
     number = {4},
     year = {1993},
     pages = { 1394-1412},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176989123}
}

Fontes, Luiz Renato G. An Ordered Phase with Slow Decay of Correlations in Continuum $1/r^2$ Ising Models. Ann. Probab., Tome 21 (1993) no. 4, pp.  1394-1412. http://gdmltest.u-ga.fr/item/1176989123/