Eur. Phys. J. B 9, 567–568 (1999) THE EUROPEAN PHYSICAL JOURNAL B c  EDP Sciences Societ` a Italiana di Fisica Springer-Verlag 1999 Erratum Non-equilibrium critical behavior of O(n)-symmetric systems U.C. T¨ auber 1, a , J.E. Santos 2 , and Z. R´ acz 3 1 Physics Department, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0435, USA 2 Institut f¨ ur Theoretische Physik, Technische Universit¨at M¨ unchen, James-Franck-Straße, 85747 Garching, Germany 3 Institute for Theoretical Physics, E¨otv¨ os University, P´ azm´any s´et´any 1/a, 1117 Budapest, Hungary Eur. Phys. J. B 7, 309-330 (1999) In Section 4.3 of reference [1], we have unfortunately ab- sorbed a factor c d k /2 0 in the definitions of the geometric factors A(d k ,d ⊥ ) and B(d k ,d ⊥ ), instead of correctly in- cluding this factor in the definition of appropriate renor- malized couplings for the non-equilibrium model J. How- ever, the coupling c 0 in general renormalizes non-trivially, which leads to a modified expression for the RG beta func- tions. Equations (4.18) and (4.50) of reference [1] should thus be replaced with e A(d k ,d ⊥ )= Γ (3 - d/2 - d k /2)Γ (d/2) 2 d-1 π d/2 Γ (d ⊥ /2) , e B(d k ,d ⊥ )= Γ (4 - d/2 - d k /2)Γ (d/2) 2 d π d/2 Γ (d ⊥ /2) · (1) The relation between the renormalized (dimensionless) coupling constants e u and eg and e u 0 and e g 0 is now given by e u = Z e u e u 0 e A(d k ,d ⊥ )μ - , e g = Z 1/2 eg eg 0 e B(d k ,d ⊥ ) 1/2 μ -ε/2 . (2) Next, we define the correct bare effective coupling con- stants e v 0 [2] and e f 0 according to ev 0 = e u 0 c d k /2 0 , e f 0 = e g 2 0 2d ⊥ λ 2 0 c d k /2 0 , (3) with their renormalized counterparts given by e v = e u c d k /2 , e f = e g 2 2d ⊥ λ 2 c d k /2 · (4) With these definitions, the expressions (4.52) to (4.58) in reference [1] have the same functional dependence on a e-mail: tauber@vt.edu ev 0 , e f 0 , e A(d k ,d ⊥ ), and e B(d k ,d ⊥ ) as they had on e u 0 , e f 0 , A(d k ,d ⊥ ), and B(d k ,d ⊥ ). In particular, in order to obtain the correct Wilson zeta functions, we merely need to sub- stitute e u by e v and e f as given in (4) into equations (4.60) to (4.65) in reference [1]. The correct beta functions to one-loop order then read β e v = e v  ζ e u - d k 2 ζ c  = e v  - + 11 6 e v - d k (104 - 38d k +3d 2 k ) 12(4 - d k ) e f ! , (5) and β e f =2 e f  ζ eg - ζ λ - d k 4 ζ c  = e f  -ε - 3d 3 k - 44d 2 k + 176d k - 96 12(4 - d k ) e f ! , (6) where we have used the fact that ζ c = -ζ λ , as given by equation (4.63) of reference [1]. To one-loop order, the finite fixed point e f * = 12(4 - d k ) 96 - 176d k + 44d 2 k - 3d 3 k ε + O(ε 2 , 2 ) (7) is positive only in the interval 0 ≤ d k ≤ 0.644838. For d k = 1, the RG flow takes the coupling constant to infinity. Therefore, the conclusions drawn in reference [1] remain valid. However, the (somewhat unphysical) expressions for the critical exponents in the expansion with respect to , ε and d k need to be corrected. To first order in d k ε, we now have e f * = ε 2  1+ 19 12 d k  , e v * = 6 11  + 13 22 d k ε, (8)