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

TL;DR

This paper explores how physical observables relate to primary scaling operators in local scale-invariance, emphasizing the role of time-dependent amplitudes and applying the theory to various non-equilibrium critical systems.

Contribution

It generalizes predictions for response and correlation functions within local scale-invariance, accounting for time-dependent amplitudes, and applies these to multiple non-equilibrium models.

Findings

Derived generalized predictions for two-time response and correlation functions.

Applied theory to models like Glauber-Ising, Ising spin glass, and contact process.

Highlighted the importance of time-dependent amplitudes in the observable-operator relationship.

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 non-equilibrium critical dynamics of several systems, with a fully disordered initial state and vanishing initial magnetization, including the Glauber-Ising model, the Frederikson-Andersen model and the Ising spin glass are discussed. The critical contact process and the parity-conserving non-equilibrium kinetic Ising model are also considered.