We explore, employing the renormalization-group theory, the critical scaling behavior of the permutation symmetric three-vector model that obeys nonconserving dynamics and has a relevant anisotropic perturbation which drives the system into a nonequilibrium steady state. We explicitly find the independent critical exponents with corrections up to two loops. They include the static exponents $\ensuremath{\nu}$ and $\ensuremath{\eta}$, the off equilibrium exponent $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\eta}}$, the dynamic exponent
z, and the strong anisotropy exponent $\mathrm{\ensuremath{\Delta}}$. We also express the other anisotropy exponents in terms of these.
Nonequilibrium short-time dynamics of first-order phase transition in a driven-disordered system at zero temperature is investigated. In a random-bond Ising model under external field, the largest discontinuous jump of order parameter shows a power-law evolution in short times: Δ M ( t ) ∼ t θ . The scaling exponent θ is equal to ( d − β/ν)/ z , where d is the dimensionality; β, ν and z are the critical exponents of the system. θ is found to be a universal exponent for any metastable relaxation in the short-time regime. This investigation suggests that the short-time dynamics is valid for the first-order phase transition in the driven disordered system and the critical phenomenon of the disordered system can be understood in the framework of nonequilibrium dynamics.