Universal short-time dynamics: Boundary functional renormalization group for a temperature quench

We present a method to calculate short-time nonequilibrium universal exponents within the functional-renormalization-group scheme. As an example, we consider the classical critical dynamics of the relaxational model A after a quench of the temperature of the system and calculate the initial-slip exponent which characterizes the nonequilibrium universal short-time behavior of both the order parameter and correlation functions. The value of this exponent is found to be consistent with the result of a perturbative dimensional expansion and of Monte Carlo simulations in three spatial dimensions.

Figure 1

Sketch of the time evolution of the magnetization $M\left(t\right)$ after a quench at $t=t_0$ from a disordered initial state with a small value $M_0$ of the magnetization to the critical temperature. The gray area indicates the time interval up to $t_m$ within which the dynamics does not display universal features.

Figure 2

Main plot: Initial-slip exponent $\theta$ as a function of the spatial dimensionality $d$, evaluated from the FRG discussed here (blue, central line) and from the $\epsilon$ expansion to first (green, lower line) and second (red upper line) order in $\epsilon =4-d$ provided in Eq. (50). The value of $\theta$ obtained from numerical Monte Carlo simulations are indicated for $d=2$ and 3 (symbols with error bars). For $d=2$, the error bars are within the symbol size. Inset: Magnification of the main plot for $d\simeq 3$.