Ordering kinetics with long-range interactions: interpolating between voter and Ising fashions
Authors: Federico Corberi, Salvatore dello Russo
Summary: We research the ordering kinetics of a generalization of the voter mannequin with long-range interactions, the p-voter mannequin, in a single dimension. It’s outlined by way of boolean variables Si, brokers or spins, positioned on websites i of a lattice, every of which takes in an elementary transfer the state of nearly all of p different brokers at distances r chosen with likelihood P(r)∝r−α. For p=2 the mannequin might be precisely mapped onto the case with p=1, which quantities to the voter mannequin with long-range interactions decaying algebraically. For 3≤p<∞, as a substitute, the dynamics falls into the universality class of the one-dimensional Ising mannequin with long-ranged coupling fixed J(r)=P(r) quenched to small finite temperatures. Within the restrict p→∞, a crossover to the (completely different) habits of the long-range Ising mannequin quenched to zero temperature is noticed.
