A NEW OF SPIN SXCHANGE DYNAMICS:COARSENING AND FRACTAL FORMATION IN PERSISTENCE

Abstract

Abstract In this thesis, we have studied two different models of global spin exchange in one dimension for the Ising spin system. In one of the models, the spins interact with their nearest neighbours and both nearest and next nearest neighbours. In the second model the spins interact with their two nearest domains. The critical dynamics of the spin systems is studied with measurables as the fraction of domain walls and the persistence probability. Persistence for the global spin exchange dynamics is studied for the first time. In addition, a study if the persistent sites are forming a fractal is presented. The fractal dimension is obtained through the box counting method and the distribution of the distances between the domains of persistent sites. Furthermore, the two-point correlation of the persistent sites and its scaling behaviour is analysed.