Critical behavior of the p-component Potts model with correlated impurities

Abstract

The problem of critical behavior in systems with correlated random impurities has recently attracted a great deal of attention. For the m-component Heisenberg model, renormalization-group calculations using a novel double expansion predict second-order transitions described by a new random fixed point, whereas the usual single μ expansion leads to a runaway, often interpreted as a smeared transition. In this paper the corresponding results for the p-state Potts model with impurities which are perfectly correlated in certain directions are presented. (For p2 the pure Potts model has a continuous transition; p=1 corresponds to the percolation problem.) In this case the new random fixed point is, in direct contrast to the m-component Heisenberg situation, never both physical and stable. Thus for the Potts model the runaway obtained in the single μ expansion persists. For sufficiently strong disorder the runaway is always obtained, even above the upper critical dimension where the Gaussian fixed point is (locally) stable. We speculate that the runaways may be symptomatic of a "smearing" of the phase transition by the strongly correlated impurities. © 1984 The American Physical Society.