Order formation processes of complex systems including different parity order parameters

Abstract

In the present study, we focus on the parity of the order parameters and clarify the order formation process in a system including two order parameters. Each order parameter shows each different parity under a gauge transformation, namely even and odd order parameters. For example, in a spin-glass model, the even order parameter corresponds to the spin-glass order parameter while the odd one corresponds to the magnetization. We introduce phenomenologically a set of Langevin equations to express the ordering process under a white Gaussian noise. Using two kinds of Fokker-Planck equations, we analyze the order formation process and the entropy production. Furthermore, we show the noise dependence of the onset time.