= Exponential complex-scalar potential
In rescaled units, $V(\phi)=-|\phi|^2+e^{\lambda|\phi|^2}$ is bounded below only for $\lambda>0$. With $s=|\phi|^2$, its derivative is $-1+\lambda e^{\lambda s}$. For $\lambda\geq1$ the unique minimum is $s=0$; for $0<\lambda<1$ the minima form a circle $s=-\ln\lambda/\lambda$. The latter phase has a massless angular <Goldstone boson> and canonical radial squared mass $-2\ln\lambda$. At $\lambda=1$ the quadratic curvature vanishes at the single symmetric minimum; that accidental critical masslessness is not a Goldstone mode.
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