Harris criterion on hierarchical lattices: Rigorous inequalities and counterexamples in Ising systems
Avishay Efrat
Abstract
Random bond Ising systems on a general hierarchical lattice are considered. The inequality between the specific heat exponent of the pure system, αp, and the crossover exponent ϕ, αp<=ϕ, gives rise to a possibility of a negative αp 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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