We study the ordering kinetics of a generalization of the voter model with long-range interactions, the p-voter model, in one dimension. It is defined in terms of Boolean variables S-i, agents or spins, located on sites i of a lattice, each of which takes in an elementary move the state of the majority of p other agents at distances r chosen with probability P(r)proportional to r(-alpha). For p = 2 the model can be exactly mapped onto the case with p = 1, which amounts to the voter model with long-range interactions decaying algebraically. For 3 <= p < infinity, instead, the dynamics falls into the universality class of the one-dimensional Ising model with long-ranged coupling constant J(r) = P(r) quenched to small finite temperatures. In the limit p -> infinity, a crossover to the (different) behavior of the long-range Ising model quenched to zero temperature is observed. Since for p > 3 a closed set of differential equations cannot be found, we employed numerical simulations to address this case.
Ordering kinetics with long-range interactions: interpolating between voter and Ising models
Corberi F.
Writing – Review & Editing
;Smaldone L.Writing – Review & Editing
2024-01-01
Abstract
We study the ordering kinetics of a generalization of the voter model with long-range interactions, the p-voter model, in one dimension. It is defined in terms of Boolean variables S-i, agents or spins, located on sites i of a lattice, each of which takes in an elementary move the state of the majority of p other agents at distances r chosen with probability P(r)proportional to r(-alpha). For p = 2 the model can be exactly mapped onto the case with p = 1, which amounts to the voter model with long-range interactions decaying algebraically. For 3 <= p < infinity, instead, the dynamics falls into the universality class of the one-dimensional Ising model with long-ranged coupling constant J(r) = P(r) quenched to small finite temperatures. In the limit p -> infinity, a crossover to the (different) behavior of the long-range Ising model quenched to zero temperature is observed. Since for p > 3 a closed set of differential equations cannot be found, we employed numerical simulations to address this case.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.