= Exponentially large correlation length in a two-dimensional spherical sigma model
{title2=$\xi\sim\Lambda^{-1}\exp[2\pi/((n-2)g_0)]$}
At $D=2$ and $n>2$, the weak-coupling <renormalization-group flow> obeys $dg/d\ell=(n-2)g^2/(2\pi)$. Integrating gives $1/g(\ell)=1/g_0-(n-2)\ell/(2\pi)$. The flow reaches order-one coupling at a length whose logarithm is $2\pi/[(n-2)g_0]+O(1)$ at this order. Restoring the microscopic scale $\Lambda^{-1}$ gives the displayed leading exponential <correlation length>. Higher loops affect its prefactor, and this conclusion does not apply to the compact $n=2$ model with its <Berezinskii–Kosterlitz–Thouless transition>.
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