Langevin dynamics of fluctuation induced first order phase transitions: self consistent Hartree Approximation

Abstract

The Langevin dynamics of a system exhibiting a Fluctuation Induced First Order Phase Transition is solved within the self consistent Hartree Approximation. Competition between interactions at short and long length scales gives rise to spatial modulations in the order parameter, like stripes in 2d and lamellae in 3d. We show that when the time scale of observation is small compared with the time needed to the formation of modulated structures, the dynamics is dominated by a standard ferromagnetic contribution plus a correction term. However, once these structures are formed, the long time dynamics is no longer pure ferromagnetic. After a quench from a disordered state to low temperatures the system develops growing domains of stripes (lamellae). Due to the character of the transition, the paramagnetic phase is metastable at all finite temperatures, and the correlation length diverges only at T=0. Consequently, the temperature is a relevant variable, for $T>0$ the system exhibits interrupted aging while for T=0 the system ages for all time scales. Furthermore, for all $T$, the exponent associated with the aging phenomena is independent of the dimension of the system.