Exact Critical Point and Critical Exponents of $\mathrm{O}\mathrm{}\left(n\right)\mathrm{}$ Models in Two Dimensions

A two-dimensional $n$-component spin model with cubic or isotropic symmetry is mapped onto a solid-on-solid model. Subject to some plausible assumptions this leads to an analytic calculation of the critical point and some critical indices for $-2\mathrm{}<~n<~2$.