(Received September 20, 1976)
A new type of fixed point two-body interactions having a typical wave vector dependence λ*ω(q,p;\hatk) is found as a solution of the renormalization group recursion relation, where ω(q,p;\hatk) ≡qi Dij (\hatk)pj (Dij(\hatk) ≡δij-\hatki \hatkj, \hatk≡k/|k|). The critical dimension dc above which long-wavelength fluctuations become Gaussian is given by 2 through simple power-counting for this interaction. The coupling constant λ* at the fixed point and correlation critical exponent η are calculated to be λ* = ε/8(m+1)K2 and η= ε/2(m+1) up to order ε respectively, where ε≡2-d, Kd ≡2-(d-1)π-d/2Γ(d/2)-1 and 2m ≡n is the number of components of the order parameters. These results are directly applicable to the stationary potential found by Grossmann for a randomly stirred fluid which obeys the Navier-Stokes equation.
URL : http://ptp.ipap.jp/link?PTP/57/1191/
DOI : 10.1143/PTP.57.1191