论文信息 - Fractal structure of zeros in hierarchical models

Fractal structure of zeros in hierarchical models

We consider an Ising and aq-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 ofq. These zeros are just the Julia set corresponding to the renormalization group transformation.

[1] Robert B. Griffiths,et al. Exactly soluble Ising models on hierarchical lattices , 1981 .

[2] P. Fatou,et al. Sur les équations fonctionnelles , 1920 .

[3] A. Erzan. Hierarchical q-state Potts models with periodic and aperiodic renormalization group trajectories , 1983 .

[4] T. D. Lee,et al. Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation , 1952 .

[5] M. Kaufman,et al. Spin systems on hierarchical lattices. Introduction and thermodynamic limit , 1982 .

[6] J. Eckmann,et al. Iterated maps on the interval as dynamical systems , 1980 .

[7] B. Mandelbrot. FRACTAL ASPECTS OF THE ITERATION OF z →Λz(1‐ z) FOR COMPLEX Λ AND z , 1980 .

[8] C. Itzykson,et al. Distribution of zeros in Ising and gauge models , 1983 .

[9] A. Nihat Berker,et al. Spin-Glass Behavior in Frustrated Ising Models with Chaotic Renormalization-Group Trajectories , 1982 .

[10] R. Pearson. Partition function of the Ising model on the periodic 4×4×4 lattice , 1982 .

[11] M. Feigenbaum. Quantitative universality for a class of nonlinear transformations , 1978 .

[12] L. Kadanoff. Notes on Migdal's recursion formulas , 1976 .