A continuum model for critical phenomena in binary mixtures subjected to long-range passive stirring is analyzed in an {ε} expansion near d=4 using the renormalization group. The random stirring destabilizes the φ⁴ fixed point and a new nonanalytic, O(ε1/2), stable fixed point appears with nonanalytic {ε} expansions for the critical exponents. The exponent governing the critical temperature lowering as a function of the stirring Reynolds number is 1.74 in d=3.
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Satten et al. (1985) studied this question.
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