For the 2d negative-coupling O(N) model at large N, the correct vacuum is a saddle point on a non-principal Riemann sheet, giving a real free energy and dynamical stability at all temperatures.
Bender, Patrick E
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On the negative coupling O(N) model in 2d at high temperature
For the 2d negative-coupling O(N) model at large N, the correct vacuum is a saddle point on a non-principal Riemann sheet, giving a real free energy and dynamical stability at all temperatures.