On the aging phenomenon in long-range spin models

The phenomenon of aging is an interesting property of non-equilibrium statistical mechanical systems whose relaxation slows down while time increases, meaning that time-translation invariance is broken. This phenomenon is observed in various systems, such as glasses and spin systems. In this work we review the aging properties of two related long-range spin models in one dimension: the voter model, where an agent copies the state of another at distance (Formula presented) (Formula presented) with a probability (Formula presented) (Formula presented), and the Ising model with the interaction between spins decaying with an analogous power law (Formula presented) (Formula presented). In particular we focus on the autocorrelation function (Formula presented) (Formula presented) and the Fisher–Huse exponent (Formula presented) (Formula presented), showing how the two models, which are equivalent in the case of nearest-neighbor interactions, behave differently as the interaction range increases (decreasing (Formula presented) (Formula presented) ).