Fractal structure of zeros in hierarchical models
Abstract
We consider an Ising and a q-state Potts model on a diamond hierarchical lattice. We give pictures of the distribution of zeros of the partition function in the complex plane of temperatures for several choices of q. These zeros are just the Julia set corresponding to the renormalization group transformation.
- Publication:
-
Journal of Statistical Physics
- Pub Date:
- December 1983
- DOI:
- 10.1007/BF01018834
- Bibcode:
- 1983JSP....33..559D
- Keywords:
-
- Zeros;
- partition function;
- hierarchical models;
- mapping;
- Julia set