Oscillatory critical amplitudes in hierarchical models

We study the oscillatory critical amplitudes of theq-states Potts model on a diamond hierarchical lattice. We consider an example of the generic case (finite critical index), as well as the degenerate case (essential singularity). In both cases, we compare the magnitude of the oscillations with geometrical characteristics of the Julia set of zeroes of the partition function.

[1]  S. Shenker,et al.  Strange objects in the complex plane , 1983 .

[2]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

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

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

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

[6]  S. Ostlund,et al.  Renormalisation-group calculations of finite systems: order parameter and specific heat for epitaxial ordering , 1979 .

[7]  R. Griffiths,et al.  Infinite susceptibility at high temperatures in the Migdal-Kadanoff scheme , 1982 .

[8]  Bernard Derrida,et al.  Fractal structure of zeros in hierarchical models , 1983 .

[9]  J. Bernasconi,et al.  Diffusion in a one-dimensional lattice with random asymmetric transition rates , 1982 .

[10]  R. Jullien,et al.  Yang-Lee edge singularity from a real-space renormalization-group method , 1979 .

[11]  W. Selke,et al.  CORRIGENDUM: Hierarchical lattice with competing interactions: an example of a nonlinear map , 1982 .

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

[13]  J. Geronimo,et al.  Meblin transforms associated with Julia sets and physical applications , 1984 .

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

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

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