Abstract
Phase transitions in a two-dimensional q-state Potts model with long-range disorder in which the correlation decays as a power law approximately r-a for separation r are studied analytically within a Migdal-Kadanoff renormalization group. Correlation terms are introduced into the parameter space of the renormalization group and the recursion relations are derived. We expand q near q0, where the specific-heat exponent of the pure system alpha p vanishes, and a near d=2. For small alpha p and delta =2-a<<1, we find three fixed points: 'pure','short-range disorder' and 'long-range disorder'. In our calculation the disorder is relevant if av-2<0 for a<d, where the v are the correlation-length exponents of the fixed points. The correlation-length exponent for the 'long-range disorder' fixed point is vlong=2/a. These are consistent with field-theoretic renormalization group results.
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