Critical dynamics of the antiferromagnetic O(3) nonlinear sigma model with conserved total magnetization

We study the near-equilibrium critical dynamics of the O(3) nonlinear sigma model describing isotropic antiferromagnets with a conserved total magnetization. To calculate response and correlation functions, we set up a description in terms of Langevin stochastic equations of motion, and their corresponding Janssen-De Dominicis response functional. We find that in equilibrium, the dynamics is well-separated from the statics to one-loop order. Since the static nonlinear sigma model is characterized by the (lower) critical dimension d_l = 2, whereas the reversible dynamical mode-coupling terms are governed by the upper critical dimension d_c= 4, a simultaneous dimensional ε expansion is not feasible, and the reversible critical dynamics for this model cannot be accessed at the static critical renormalization group fixed point. However, in the coexistence limit, we can perform the ε = 4 - d expansion near d_c, whereupon we recover the asymptotic dynamic exponents previously determined for the O(n)-symmetric Sasvári-Schwabl-Szépfalusy model in the ordered phase.