A Method to Control Order of Phase Transition: Invisible States in Discrete Spin Models

Abstract: It is an important topic to investigate nature of the phase transition in wide area of science such as statistical physics, materials science, and computational science. Recently it has been reported the efficiency of quantum adiabatic evolution/quantum annealing for systems which exhibit a phase transition, and we cannot obtain a good solution in such systems. Thus, to control the nature of the phase transition has been also attracted attention in quantum information science. In this paper we review nature of the phase transition and how to control the order of the phase transition. We take the Ising model, the standard Potts model, the Blume-Capel model, the Wajnflasz-Pick model, and the Potts model with invisible states for instance. Until now there is no general method to avoid the difficulty of annealing method in systems which exhibit a phase transition. It is a challenging problem to propose a method how to erase or how to control the nature of the phase transition in the target system.