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| -rw-r--r-- | bezout.tex | 3 |
1 files changed, 2 insertions, 1 deletions
@@ -45,7 +45,7 @@ At any critical point $\epsilon=H/N$, the average energy. When compared with $z^*z=N$, the constraint $z^2=N$ may seem an unnatural extension of the real $p$-spin spherical model. However, a model with this nonholomorphic spherical constraint has a disturbing lack of critical points -nearly everywhere, since $0=\partial H/\partial z^*=-p\epsilon z$ is only +nearly everywhere, since $0=\partial^* H=-p\epsilon z$ is only satisfied for $\epsilon=0$, as $z=0$ is forbidden by the constraint. Since $H$ is holomorphic, a point is a critical point of its real part if and @@ -77,6 +77,7 @@ form = \int dx\,dy\,\delta(\mathop{\mathrm{Re}}\partial H)\delta(\mathop{\mathrm{Im}}\partial H) |\det\partial\partial H|^2. \end{equation} +$\langle|\partial_i\partial_j H_0|^2\rangle=p(p-1)|z|^2/2N$ and $\langle(\partial_i\partial_j H_0)^2\rangle=p(p-1)\kappa z^2/2N$ \bibliographystyle{apsrev4-2} \bibliography{bezout} |