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

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

2001-04-22

arxiv.org/abs/cond-mat/0104407v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, 3 figures

Scientific paper

10.1103/PhysRevE.63.066112

Random bond Ising systems on a general hierarchical lattice are considered. The inequality between the specific heat exponent of the pure system, $\alpha_p$, and the crossover exponent $\phi$, $\alpha_p<=\phi$, gives rise to a possibility of a negative $\alpha_p$ along with a positive $\phi$, 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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