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author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2020-12-09 15:24:16 +0100 |
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committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2020-12-09 15:24:16 +0100 |
commit | 3ee1888e22f2571011de7aabd602502d89062cb5 (patch) | |
tree | 549fd444ef5a3dd480be29bf9357d73220a1d463 | |
parent | 5f9db45efcf9ffb2d97a854185a1c505d66b20d2 (diff) | |
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Fixed an unclosed "teal" environment.
-rw-r--r-- | bezout.tex | 2 |
1 files changed, 1 insertions, 1 deletions
@@ -345,7 +345,7 @@ is the logarithm of the number of configurations of a given $(a,H_0)$. This problem may be solved exactly with replicas, {\em but it may also be simulated} \cite{Bray_1980_Metastable}. Consider for example the ground-state energy for given $a$, that is, the energy in the limit $\beta_R \rightarrow \infty$ taken adjusting $\beta_I$ so that $\Im H_0=0$ . For $a=1$ this coincides with the ground-state of the real problem. -{\color{teal} {\bf somewhere} In Figure \ref{fig:desert} we show that for $\kappa<1$ there is always a gap of $a$ close to one for which there are no solutions: this is natural, given that the $y$ contribution to the volume shrinks to zero as that of an $N$-dimensional sphere $\sim(a-1)^N$. +{\bf somewhere} In Figure \ref{fig:desert} we show that for $\kappa<1$ there is always a gap of $a$ close to one for which there are no solutions: this is natural, given that the $y$ contribution to the volume shrinks to zero as that of an $N$-dimensional sphere $\sim(a-1)^N$. For the case $K=1$ -- i.e. the analytic continuation of the usual real computation -- the situation is more interesting. In the range of values of $\Re H_0$ where there are exactly real solutions this gap closes, and this is only possible if the density of solutions diverges at $a=1$. Another remarkable feature of the limit $\kappa=1$ is that there is still a gap without solutions around |