Renormalization Group for Large N Strongly Commensurate Dirty Boson Model

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 $ϵ=D-2-d\mathrm{/}2$. 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.