The basic features of the slow relaxation phenomenology arising in phase ordering processes are obtained analytically in the large N model through the exact separation of the order parameter into the sum of thermal and condensation components. The aging contribution in the response function χ ag (t, t w ) is found to obey a pattern of behavior, under variation of dimensionality, qualitatively similar to the one observed in Ising systems. There exists a critical dimensionality (d = 4) above which χ ag (t, t w ) is proportional to the defect density ρ D (t), while for d < 4 it vanishes more slowly than ρ D (t) and at d = 2 does not vanish. As in the Ising case, this behavior can be understood in terms of the dependence on dimensionality of the interplay between the defect density and the effective response associated to a single defect.

We derive for Ising spins an off-equilibrium generalization of the fluctuation dissipation theorem, which is formally identical to the one previously obtained for soft spins with Langevin dynamics [L.F. Cugliandolo, J. Kurchan, and G. Parisi, J. Phys. I 4, 1641 (1994)]. The result is quite general and holds both for dynamics with conserved and nonconserved order parameters. On the basis of this fluctuation dissipation relation, we construct an efficient numerical algorithm for the computation of the linear response function without imposing the perturbing field, which is alternative to those of Chatelain [J. Phys. A 36, 10 739 (2003)] and Ricci-Tersenghi [Phys. Rev. E 68, 065104(R) (2003)]. As applications of the new algorithm, we present very accurate data for the linear response function of the Ising chain, with conserved and nonconserved order parameter dynamics, finding that in both cases the structure is the same with a very simple physical interpretation. We also compute the integrated response function of the two-dimensional Ising model, confirming that it obeys scaling chi (t, t(w)) approximately equal to t(-a)(w) f (t/t(w)) , with a =0.26+/-0.01 , as previously found with a different method.

The behavior of a phase separating binary mixture in uniform shear flow is investigated by numerical simulations and in a renormalization group (RG) approach. Results show the simultaneous existence of domains of two characteristic scales. Stretching and cooperative ruptures of the network produce a rich interplay where the recurrent prevalence of thick and thin domains determines log-time periodic oscillations. A power law growth R(t) ∼ t α of the average domain size, with α = 4/3 and α = 1/3 in the flow and shear direction respectively, is shown to be obeyed. numbers: 47.20Hw; 05.70Ln; 83.50Ax The application of a shear flow to a disordered binary mixture quenched into a coexistence region greatly affects the phase-separation process [1]. A large anisotropy is observed in typical patterns of domains which appear greatly elongated in the direction of the flow [2]. This behavior has consequences for the rheological properties of the mixture. A rapid strain-induced thickening followed by a gradual thinning regime is observed [3]. Various numerical simulations confirm these observations [4][5][6]. PACSIn a recent paper [7] we have studied the phaseseparation kinetics in the context of a self-consistent approximation, also known as large-N limit. Within this approach the existence of a scaling regime characterized by an anisotropic power-law growth of the average size of domains was established. The segregation process, however, cannot be fully described by this technique because interfaces are absent for large-N [8].The aim of this letter is to investigate the ordering process by extensive numerical simulations. Our main result concerns the simultaneous existence of two length scales which characterize the thickness of the growing domains. The competition between these scales produces a rich dynamical pattern with an oscillatory behavior due to the cyclical prevalence of one of the two lengths. A power law growth R(t) ∼ t α of the average domain size, with α = 4/3 and α = 1/3 in the flow and shear direction respectively, is shown to be obeyed by a renormalization group (RG) analysis.The kinetic behaviour of the binary mixture is described by the Langevin equationwhere the scalar field ϕ represents the concentration difference between the two components of the mixture [1]. The equilibrium free-energy can be chosen as usual to bewhere b, κ > 0 and a < 0 in the ordered phase. v is an external velocity field describing plane shear flow with average profile given bywhere γ is the shear rate and e x is the unit vector in the flow direction. η is a gaussian white noise, representing thermal fluctuations, with mean zero and correlation η( r, t)η( r ′ , t ′ ) = −2T Γ∇ 2 δ( r − r ′ )δ(t − t ′ ), where Γ is a mobility coefficient, T is the temperature of the fluid, and the symbol ... denotes the ensemble average. The Langevin equation (1) has been simulated in d = 2 by first-order Euler discretization scheme. Periodic boundary conditions have been used in the flow direction while in the y direction the point at (x, y) is i...