A New Quenched $XY$ model with Nonusual "Exotic" Interactions

Abstract

Human beings live in a networked world in which information spreads very fast thanks to the advances in technology. In the decision processes or opinion formation there are different ideas of what is collectively good but they tend to go against the self interest of a large amount of agents. Here we show that the associated stochastic operator ($\mathfrak{\widehat{W^\aleph}}_{\rho,\Delta,r}$) proposed in [43] for describe phenomena, does not belong to a CP (Contact Processes) universality class [35]. However, its mathematical structure corresponds to a new Exotic quantum XY model, but unprecedently, their parameters is a "function" of the interaction between the local sities $(i-1,i,i+1)$, and with the impurity present at the same site $i$.