Aging-induced continuous phase transition

Abstract

Aging is considered as the property of the elements of a system to be less prone to change states as they get older. We incorporate aging into the noisy voter model, a stochastic model in which the agents modify their binary state by means of noise and pair-wise interactions. Interestingly, due to aging the system passes from a finite-size discontinuous transition between ordered (ferromagnetic) and disordered (paramagnetic) phases to a second order phase transition, well defined in the thermodynamic limit, belonging to the Ising universality class. We characterize it analytically by finding the stationary solution of an infinite set of mean field equations. The theoretical predictions are tested with extensive numerical simulations in low dimensional lattices and complex networks. We finally employ the aging properties to understand the symmetries broken in the phase transition.

Ordering dynamics in the voter model with aging

“…Again, it would seem naively that reducing the number of interactions amongst agents should impede the reaching of consensus, but it was shown that exactly the opposite happens, namely the consensus is reached more easily in such an scenario of aging. In a recent paper by some of us [49,50], it was shown that the inclusion of aging in the noisy version of the voter model [7,51,52] induces a state of imperfect consensus that remains in the thermodynamic limit. Another study of the noiseless voter model [43] focused on the distribution of the time between individual changes of states C(t), which in turn is related with the activation probability p i , or the age-dependent probability of interaction.…”

Reduction from non-Markovian to Markovian dynamics: the case of aging in the noisy-voter model

“…The inertia of individuals affecting its willingness to change state by imitation was introduced in reference [36] in the context of the noiseless voter model and it was later generalized in reference [40] under the presence of noise. The basic idea is to introduce a mechanism, inertia or aging, by which agents are less prone to copy a neighbor's state the longer they have been holding their current state.…”

“…(21). ‡ In [40] we used the notation f (a, x) to stress the dependence on a of this function. § The expression is f aging (…”

“…Given the form G st (n) ∼ e −N V (n/N ) , the dependence with system size N of the moments of the magnetization m k st near the critical point a = a c can be obtained [43] from the In Ref. [40] we used b = 1, c = 2 and obtained a critical value a c = 0.07556 . .…”

“…Recent studies of the Markovian version of the model include: the effect of a network structure [27,28], external control of the system [29,30], the role of zealots [31] and contrarians [32], more than two states [33,34], and first-passage properties [35]. Different non-Markovian versions have been studied as well for the model without noise [36,37,38,39] and with noise [40] (see [41] for a recent review of the model, both…”