Renormalization-group description of nonequilibrium critical short-time relaxation processes: A three-loop approximation

Abstract

The influence of nonequilibrium initial values of the order parameter on its evolution at a critical point is described using a renormalization group approach of the field theory. The dynamic critical exponent θ ′ of the short time evolution of a system with an n-component order parameter is calculated within a dynamical dissipative model using the method of ε-expansion in a threeloop approximation. Numerical values of θ ′ for three-dimensional systems are determined using the Padé-Borel method for the summation of asymptotic series.

Short-time dynamics of finite-size mean-field systems

“…(34). In any case the behavior ∆m (2) ∼ ǫt up to t ∼ t * is consistent with the STD scaling hypothesis for the set of mean-field exponents zν = 2, β = 1/2, d c = 6 and in agreement with numerical outcomes [6].…”

“…On the contrary, when m 0 ≪ 1, a relatively large number of trajectories cross the barrier between minima and m (2) approaches the equilibrium value (which is larger than the steady one), even at very short times, as can be verified by comparing the numerical plateaux in…”

“…The short-time universal scaling behavior has been verified in a large variety of critical systems both by renormalization group (RG) calculations [1,2] and Monte Carlo (MC) numerical simulations [3][4][5]. The hypothesis also applies when the system starts in the completely ordered state, i.e., m 0 = 1.…”

Universal amplitudes ratios for critical aging via functional renormalization group

“…By solving Eqs. (44) for the reduced response and correlation function, R and C, respectively, one obtains a form similar to the one given in Eq. ( 41) in the aging regime, using the fact that D k /Z k = const., which is a consequence of the fact that the flow equation of D k and Z k are identical 32 (the constant can then be reabsorbed in a suitable renormalization of the fields).…”

“…IV B applies, upon replacing r k with r k /Z k in Eqs. (44). A canonical power counting shows that r/Z has the dimension of an inverse time, and therefore equations similar to Eqs.…”