The Julia sets and complex singularities in hierarchical Ising models
Bleher, Pavel ; Lyubich, Mikhail
arXiv, 9201275 / Harvested from arXiv
Text on arXiv
We study the analytical continuation in the complex plane of free energy of the Ising model on diamond-like hierarchical lattices. It is known that the singularities of free energy of this model lie on the Julia set of some rational endomorphism $f$ related to the action of the Migdal-Kadanoff renorm-group. We study the asymptotics of free energy when temperature goes along hyperbolic geodesics to the boundary of an attractive basin of $f$. We prove that for almost all (with respect to the harmonic measure) geodesics the complex critical exponent is common, and compute it.
Publié le : 1990-09-25
Classification:  Mathematics - Dynamical Systems,  Mathematical Physics 
@article{9201275,
     author = {Bleher, Pavel and Lyubich, Mikhail},
     title = {The Julia sets and complex singularities in hierarchical Ising models},
     journal = {arXiv},
     volume = {1990},
     number = {0},
     year = {1990},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9201275}
}

Bleher, Pavel; Lyubich, Mikhail. The Julia sets and complex singularities in hierarchical Ising models. arXiv, Tome 1990 (1990) no. 0, . http://gdmltest.u-ga.fr/item/9201275/