On the identification of quasiprimary scaling operators in local scale-invariance

Abstract

Abstract. The relationship between physical observables defined in lattice models and the associated (quasi-)primary scaling operators of the underlying field-theory is revisited. In the context of local scale-invariance, we argue that this relationship is only defined up to a time-dependent amplitude and derive the corresponding generalizations of predictions for two-time response and correlation functions. Applications to nonequilibrium critical dynamics of several systems, with a fully disordered initial state and vanishing initial magnetization, including the Glauber-Ising model, the FrederiksonAndersen model and the Ising spin glass are discussed. The critical contact process and the parity-conserving non-equilibrium kinetic Ising model are also considered.

Ageing in the contact process: scaling behaviour and universal features

“…(See, e.g., figure 2 in [10].) On the other hand, the field-theoretical results presented here are free from numerical artefacts and corrections to scaling, which were invoked in [11] to explain the findings of [10].…”

“…A more general version of LSI [11] -the version we shall refer to in this paper -improved considerably the agreement with simulations while the disagreement with field-theoretical predictions remained. Also in the case of the CP, numerical results indicate that the scaling function f R predicted by LSI is incorrect for t ≃ s [10,11]. It was suggested in [11,23] that one could possibly account for this discrepancy by extending LSI to include also the case of a nonvanishing average of the order parameter (in the present version a vanishing order parameter is implicitly assumed).…”

“…However, in the case of critical ageing of the Ising model with purely relaxational dynamics, it was shown that corrections to the prediction of LSI are present both in field-theoretical results at two loops [13,20] and in simulations [21,22]. A more general version of LSI [11] -the version we shall refer to in this paper -improved considerably the agreement with simulations while the disagreement with field-theoretical predictions remained. Also in the case of the CP, numerical results indicate that the scaling function f R predicted by LSI is incorrect for t ≃ s [10,11].…”

“…Also in the case of the CP, numerical results indicate that the scaling function f R predicted by LSI is incorrect for t ≃ s [10,11]. It was suggested in [11,23] that one could possibly account for this discrepancy by extending LSI to include also the case of a nonvanishing average of the order parameter (in the present version a vanishing order parameter is implicitly assumed). As this extension is at present still lacking, in what follows we shall refer to the available version of LSI.…”

“…The directed percolation (DP) universality class has been recently the subject of renewed interest in the context of ageing phenomena [8,9,10,11], which are characterized by two-time quantities (such as response and correlation functions, see below) which are homogeneous functions of their time arguments and do not display the time-translational invariance which is expected in a stationary state. The two-time quantities of interest are the connected density-density correlation function C x−x ′ (t, s) := n x (t)n x ′ (s) − n x (t) n x ′ (s) and the response function R x−x ′ (t, s) := δ n x (t) /δκ x ′ (s)| κ=0 where κ x ′ (s) is the field conjugate to n x ′ (s) -corresponding to a local spontaneous activation rate of the lattice site x ′ at time s -and .…”