23 research outputs found
The Julia sets and complex singularities in hierarchical Ising models
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 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 . We
prove that for almost all (with respect to the harmonic measure) geodesics the
complex critical exponent is common, and compute it
Spectra of weighted composition operators on algebras of analytic functions on Banach spaces
summary:Let be a complex Banach space, with the unit ball . We study the spectrum of a bounded weighted composition operator on determined by an analytic symbol with a fixed point in such that is a relatively compact subset of , where is an analytic function on