We study the off-equilibrium response and correlation functions and the corresponding fluctuation-dissipation ratio for a purely dissipative relaxation of an $O\left(N\right)\mathrm{}$ symmetric vector model (model $A)$ below its upper critical dimension. The scaling behavior of these quantities is analyzed and the associated universal functions are determined at first order in $\epsilon =4\mathrm{}-d$ in the high-temperature phase and at criticality. A nontrivial limit of the fluctuation-dissipation ratio is found in the aging regime $X^{\infty }=1/2\mathrm{}\left(1-\right(\epsilon /4\left)\right(N+2\mathrm{})/(N+8\mathrm{}\left)\mathrm{}\right)+O\left({\epsilon }^2\right).\mathrm{}$

• Received 19 March 2002

DOI:https://doi.org/10.1103/PhysRevE.65.066120