Decelerating microdynamics accelerates macrodynamics in the voter model

We study an extension to the standard voter model, in which voters have an individual inertia to change their state. We assume that this inertia increases with the time a voter has been in its current state. Increasing the level of inertia in the system decelerates the microscopic dynamics. Counter-intuitively, we find that the time to reach a macroscopic ordered state can be accelerated for intermediate levels of inertia. This is true for different network topologies, including fully-connected ones. We derive a mean-field approach that shows that the origin of this phenomenon is the break of the magnetization conservation because of the evolving inertia. We find that the dynamics near the ordered state is governed by two competing processes, which stabilize either the majority or the minority of voters. If the first one dominates, it accelerates the ordering of the system. PACS 02.50.Ey, 64.60.De, 89.65.-s The voter model [11] has served as a paragon for the emergence of an ordered state in a non-equilibrium system, with numerous inter-disciplinary applications, e.g. in chemical kinetics [10], ecological systems [4, 13, 14, 15], and social systems [3, 8]. It denotes a simple binary system comprised of N voters, each of which can be in one of two states (often referred to as opinions), σi = ±1. The dynamics reads as follows: A voter is selected at random and adopts the state of a randomly chosen neighbor. After N such update events, time is increased by 1. Starting with a random assignment of states to the voters, the key question is then whether the system can reach an ordered state (called consensus) in which all voters have adopted the same σ. The average time Tκ to reach consensus depends (i) on the system size N and (ii) the topology of the network, which recently gained much attention in the physics community [1, 17, 19]. But also the coarsening dynamics in spatially extended systems, i.e. the formation and growth dynamics of state domains was studied and compared to other phase transitions [3, 5, 6]. Among its prominent properties, the magnetization conservation was extensively studied [2, 7, 16, 18]. In this Letter, we extend the standard voter model dynamics by assuming that an individual voter has a certain inertia νi to change its state. νi increases with the persistence time τi which is the time elapsed since the last change of state. The longer the voter already