Harris criterion for direct and orthogonal quenched randomness

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Abstract
Critical-behavior stability is studied, with respect to the introduction of quenched randomness that is direct (e.g., field randomness at field approach to criticality) or orthogonal (e.g., field randomness at temperature approach to criticality). Rather than resorting to renormalization-group theory, an argument is conducted by considering the effective uniform field per spin within a correlated region. By comparing the correlation lengths limited by this effective uniform field and by the actual uniform deviation from criticality, it is recovered that nonrandom critical behavior is not maintained under random fields when its susceptibility critical exponent γ is positive, and conversely.