Critical aging of a ferromagnetic system from a completely ordered state

We adapt the nonlinear σ model to study the nonequilibrium critical dynamics of $\ab{O}(n)$ symmetric ferromagnetic system. Using the renormalization group analysis in $d=2+\varepsilon$ dimensions we investigate the pure relaxation of the system starting from a completely ordered state. We find that the average magnetization obeys the long-time scaling behaviour almost immediately after the system starts to evolve while the correlation and response functions demonstrate scaling behaviour which is typical for aging phenomena. The corresponding fluctuation-dissipation ratio is computed to first order in ε and the relation between transverse and longitudinal fluctuations is discussed