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 …

Several examples are given of soluble models of phase-transition phenomena utilizing
classical discrete spin systems with nearest-neighbor interaction on hierarchical lattices …

We study the oscillatory critical amplitudes of the q-states Potts model on a diamond
hierarchical lattice. We consider an example of the generic case (finite critical index), as well …

A proper description of spin glass remains a hard subject in theoretical physics and is
considered to be closely related to the emergence of chaos in the renormalization group …

The finite q-difference operator lends itself naturally to describing systems with exact
discrete dilatation symmetry, such as hierarchical lattices. We express the homogeneity …

We study the phase transition of the Potts model on diamond-like hierarchical lattices. It is
shown that the set of the complex singularities is the Julia set of a rational mapping. An …

The fractional Potts model on diamond‐like hierarchical lattices is introduced in this
manuscript, which is a fractional rational system in the complex plane. Then, the fractal …

Feigenbaum Julia sets of singularities of free energy Page 1 Ergod. Th. & Dynam. Sys. (2010),
30, 1573–1591 c 2009 Cambridge University Press doi:10.1017/S0143385709000522 Printed …

For simple Statistical models, the partition function on a finite lattice appears as a polynomial
in one or two variables. The location of its zeroes offers a convenient way to visualize its …

The two-dimensional renormalization map of the diamond-hierarchical Ising model in an
external field is given, and pictures of the distribution of zeros of the partition function in the …