The large- $N$ $\ensuremath{\sigma}$ 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 $\ensuremath{\epsilon}=D\ensuremath{-}2\ensuremath{-}d/2.$ In particular, it is found that $\ensuremath{\nu}d=2.$ When $D=d+1,$ this model is equivalent to a large- $N$ limit of the strongly commensurate dirty boson problem.The large-$N$ $\ensuremath{\sigma}$ 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 $\ensuremath{\epsilon}=D\ensuremath{-}2\ensuremath{-}d/2.$ In particular, it is found that $\ensuremath{\nu}d=2.$ When $D=d+1,$ this model is equivalent to a large-$N$ limit of the strongly commensurate dirty boson problem.

arXiv:cond-mat/9809244Physical review. B, Condensed matterOct 1, 19996 citations

Comments on renormalization group series

A. J. F. Siegert, David J. Vezzetti, Harvey S. Leff

Physica A Statistical Mechanics and its ApplicationsNov 1, 19770 citations

Renormalization-group treatment of the large-

N

t

J

model

The large-

N

$\ensuremath{\sigma}$ 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 $\ensuremath{\epsilon}=D\ensuremath{-}2\ensuremath{-}d/2.$ In particular, it is found that $\ensuremath{\nu}d=2.$ When

D=d+1,

this model is equivalent to a large-

N

limit of the strongly commensurate dirty boson problem.