Quench Disorder and Scalar Field Theory in the Presence of Boundary

Abstract: Disordered systems are interesting for many physical reasons. In this article, we study the renormalization group property of quenched disorder systems in the presence of a boundary. We construct examples of scalar field theories in various dimensions with both classical and quantum disorder localized at the boundary. We study these theories in $\e$-expansion and discuss properties of fixed points of the renormalization group flow.