A self-avoiding walk exponent bound on the thermal Ising exponent on some hierarchical lattices
- 1 January 1985
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 18 (1) , L17-L23
- https://doi.org/10.1088/0305-4470/18/1/004
Abstract
Calculation of critical exponents on a simple class of hierarchical lattice reveals that lambda s>or= lambda t, where lambda s is the self-avoiding walk fixed point eigenvalue and lambda t the Ising thermal eigenvalue. High-dimensional limits of some families of hierarchies obey lambda t to lambda s as D to infinity ; this convergence replaces the Euclidean concept of upper critical dimension on these lattices. However, families of hierarchies for which D to infinity but with constant connectivity do not show this convergence.Keywords
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