Renormalization Group for Large N Strongly Commensurate Dirty Boson Model

TL;DR

This paper analyzes a large N sigma model with disorder using renormalization group techniques, calculating critical exponents and establishing a connection to the strongly commensurate dirty boson problem in certain dimensions.

Contribution

It provides a comprehensive RG analysis of the large N sigma model with disorder, including all-order calculations of critical exponents and links to dirty boson physics.

Findings

Critical exponent relation: νd=2.

All-order calculation of critical exponents.

Equivalence to large N limit of dirty boson model when D=d+1.

Abstract

The large N sigma model, in D<4 space-time dimensions, with disorder a function of d space dimensions, is analyzed via a renormalization group treatment. Critical exponents for average quantities are calculated, first to lowest order and then to all orders, in $\epsilon=D-2 - d/2$. In particular, it is found that $\nu d =2$. When D=d+1, this model is equivalent to a large N limit of the strongly commensurate dirty boson problem.