Scaling theory of nonlinear critical relaxation

A scaling analysis of nonlinear critical slowing down on the basis of a Landau-type relaxation equation, shows that the critical exponents, Δ⁽ˡ⁾ and Δ⁽ⁿˡ⁾ of the linear and nonlinear relaxation times of the order parameter are related by Δ⁽ⁿˡ⁾=Δ⁽ˡ⁾-β. Generally if Q scales like ΔT^βQ one has ΔQ⁽ˡ⁾-ΔQ⁽ⁿˡ⁾=βQ but a different relaxation may occur in systems with oscillatory modes.