O(n)Heisenberg Model Close ton=d=2

Abstract

The critical behavior of the $O\left(n\right)\mathrm{}$ classical Heisenberg model in $d$ dimensions close to $n=d=2\mathrm{}$ is discussed, assuming analyticity in $n$ and $d$ of the renormalization-group equations. In the ($d$,$n$) plane there is a line passing through (2,2) across which the critical exponents are nonanalytic. For $d=2\mathrm{} \mathrm{and} -2\mathrm{}<~n<~2$, a conjecture is presented for the exact form of the leading and subdominant thermal eigenvalues.