MAGNETIC-SUSCEPTIBILITY OF O(N) SIGMA-MODELS IN 2D - WEAK-COUPLING RESULTS FROM 1/N EXPANSION

The magnetic susceptibilities of the non-linear sigma-models in 2D are given to three leading orders in 1/N as functions of the inverse bare coupling beta and up to correlation lengths 150. Within the systematic error introduced by truncating the 1/N expansion, our results agree with Monte Carlo results for N greater-than-or-equal-to 3. We argue that the 1/N series is convergent with a beta-dependent radius of convergence approaching 1/2 at weak coupling, and use this to predict the value for the magnetic susceptibility at asymptotically weak coupling. Our calculation features "Fourier accelerated" numerical evaluation of Feynman diagrams, and extrapolation of finite volume results to infinite volume by phenomenological scaling.