Critical Phenomena of Isolated Systems

Abstract

Regarding the order parameter as the “field component,” we see the semi-dual variational structure in phase field equations associated with several critical phenomena. Particularly, the nonlinear eigenvalue problem with non-local term arises as the stationary state of the closed system. Recognizing the profile of the total set of stationary solutions and distinguishing their stability and instability are the first step to clarify the process of self-organization. In this chapter we study these variational structures sealed in several mathematical models of self-assembly.