Equations of State for Nonlinear Sigma-Models II: Relations between Resummation Schemes, and Crossover Phenomena

TL;DR

This paper connects a new resummation method for nonlinear sigma-models with renormalization group solutions, extending equations of state to models with crossover phenomena, exemplified by symmetry crossover in localization models.

Contribution

It introduces a relation between resummation schemes and RG solutions, enabling the analysis of crossover phenomena in nonlinear sigma-models.

Findings

Established a link between resummation methods and RG equations.

Extended equations of state to models with crossover phenomena.

Analyzed symmetry crossover in localization models.

Abstract

It is shown how a recent method to systematically extrapolate and resum the loop expansion for nonlinear sigma-models is related to solutions of the renormalization group equation. This relation is used to generalize the explicit equations of state obtained previously to models which display crossover phenomena. As an example we discuss Wegner's localization model and consider the crossover from symplectic to unitary symmetry.