Calculation of Critical Slowing Down Exponent Using Wilson's Expansion Methods

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The parameter 0' is the effective potentialrange2>,a>,4> defined by a=s for O 2, when the interaction strength takes the inverse power law form J(R) =J0R· (>0). The quantity U[s] is some functional of s (.x, t) and· h denotes a time-dependent reduced magnetic field H(.x, t) I (kBT). Now we are interested in the critical slowing down of the order parameter, which is characterized by the relaxation time defined5> by

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