The Julia sets and complex singularities in hierarchical Ising models

Details The Julia sets and complex singularities in hierarchical Ising models The Julia sets and complex singularities in hierarchical Ising models

1990-09-26

arxiv.org/abs/math/9201275v1

Mathematics

Dynamical Systems

Scientific paper

10.1007/BF02102810

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.

Affiliated with

Also associated with

No associations

Rating

The Julia sets and complex singularities in hierarchical Ising models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Julia sets and complex singularities in hierarchical Ising models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Julia sets and complex singularities in hierarchical Ising models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-75890