A New Type of Fixed Point Interactions Having Wave Vector-Dependent Structure

概要

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A new type of fixed point two-body interactions having a typical wave vector dependence λ*w(q,p;k^^^) is found as a solution of the renormalization group recursion relation, where w(q, p; k^^^)≡q_iD_<ij>(k^^^)p_j (D_<ij>(k^^^)≡δ_<ij>-k^^^_ik^^^j, k^^^≡k/|k|). The critical dimension d_c 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)K_2 and η=ε/2(m+1) up to order ε respectively, where ε≡2-d, K_d≡2^<-(d-1)>π^<-d/2>Γ(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.
理論物理学刊行会の論文
1977-04-25