Disordered Lattice Glass $\phi^{4}$ Quantum Field Theory

Abstract

We study numerically the three-dimensional $\phi^{4}$ spin glass, a prototypical disordered and discretized Euclidean field theory that manifests inhomogeneities in space and time but considers a homogeneous squared mass and lambda terms. The $\phi^{4}$ lattice glass field theory is a conceptual generalization of spin glasses to continuous degrees of freedom and we discuss the existence of a limit under which it formally reduces to the Edwards-Anderson model. By defining four variants of an order parameter which are suitable for continuous spin glasses, we verify numerically the emergence of an overlap in absence of the magnetization thus confirming the presence of a spin glass phase transition for a value of a critical squared mass. We conclude by discussing how the $\phi^{4}$ spin glass can be utilized to address assumptions of complete homogeneity in space or time and how, in parallel to statistical physics, provides a suitable framework to investigate the nonperturbative dynamics of machine learning algorithms from the perspective of disordered lattice and constructive field theory.