Hierarchical lattices: some examples with a comparison of intrinsic dimension and connectivity and Ising model exponents

1983 ◽  
Vol 16 (13) ◽  
pp. 3077-3083 ◽  
Author(s):  
J R Melrose
Keyword(s):  
Ising Model ◽  
Intrinsic Dimension ◽  
Hierarchical Lattices

scholarly journals Transfer matrix approach to the disordered Ising model on hierarchical lattices

2006 ◽  
Vol 73 (17) ◽  
Author(s):  
Danielle O. C. Santos ◽  
Edvaldo Nogueira ◽  
Roberto F. S. Andrade
Keyword(s):  
Ising Model ◽  
Transfer Matrix ◽  
Matrix Approach ◽  
Transfer Matrix Approach ◽  
Hierarchical Lattices

scholarly journals FIELD BEHAVIOR OF AN ISING MODEL WITH APERIODIC INTERACTIONS

2000 ◽  
Vol 14 (14) ◽  
pp. 1473-1480
Author(s):  
ANGSULA GHOSH ◽  
T. A. S. HADDAD ◽  
S. R. SALINAS
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Ising Model ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Exchange Interactions ◽  
Universality Class ◽  
Recursion Relations ◽  
Hierarchical Lattices ◽  
Exact Renormalization Group

We derive exact renormalization-group recursion relations for an Ising model, in the presence of external fields, with ferromagnetic nearest-neighbor interactions on Migdal–Kadanoff hierarchical lattices. We consider layered distributions of aperiodic exchange interactions, according to a class of two-letter substitutional sequences. For irrelevant geometric fluctuations, the recursion relations in parameter space display a nontrivial uniform fixed point of hyperbolic character that governs the universal critical behavior. For relevant fluctuations, in agreement with previous work, this fixed point becomes fully unstable, and there appears a two-cycle attractor associated with a new critical universality class.

Magnetization in the ising model on hierarchical lattices

1988 ◽  
Vol 74 (3) ◽  
pp. 320-323
Author(s):  
V. P. Bovin ◽  
I. Ya. Shneiberg
Keyword(s):  
Ising Model ◽  
Hierarchical Lattices
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