Critical phenomena in randomly stirred fluids

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 ${\mathrm{\phi }}^4$ fixed point and a new nonanalytic, O(${\mathrm{\epsilon }}^{1/2}$), 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.