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Harris criterion on hierarchical lattices: Rigorous inequalities and counterexamples in Ising systems

Avishay Efrat
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Abstract

Random bond Ising systems on a general hierarchical lattice are considered. The inequality between the specific heat exponent of the pure system, $α_p$, and the crossover exponent $ϕ$, $α_p<=ϕ$, gives rise to a possibility of a negative $α_p$ along with a positive $ϕ$, leading to random criticality in disagreement with the Harris criterion. An explicit example where this really happens for an Ising system is presented and discussed. In addition to that, it is shown that in presence of full long-range correlations, the crossover exponent is larger than in the uncorrelated case.

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BibTeXRIS

Avishay Efrat. 2001-04-22. Harris criterion on hierarchical lattices: Rigorous inequalities and counterexamples in Ising systems. https://doi.org/10.1103/physreve.63.066112

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