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| author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2022-07-13 13:33:04 +0200 |
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| committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2022-07-13 13:33:04 +0200 |
| commit | 835a7763c2bc061251bf8a678037ef0ab3a614ba (patch) | |
| tree | 4f8b43a8c5ddd55ea29e22778c0a1b5bcbc30936 /frsb_kac-rice.tex | |
| parent | 8bc5cec374682cf79d78f12e37ad2519285b58bb (diff) | |
| download | PRE_107_064111-835a7763c2bc061251bf8a678037ef0ab3a614ba.tar.gz PRE_107_064111-835a7763c2bc061251bf8a678037ef0ab3a614ba.tar.bz2 PRE_107_064111-835a7763c2bc061251bf8a678037ef0ab3a614ba.zip | |
Slightly nicer typesetting of bad equations.
Diffstat (limited to 'frsb_kac-rice.tex')
| -rw-r--r-- | frsb_kac-rice.tex | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex index 7e260f9..752a7ae 100644 --- a/frsb_kac-rice.tex +++ b/frsb_kac-rice.tex @@ -860,9 +860,9 @@ as we expand the extremal conditions, using \eqref{eq:replica.det.cont} to treat the determinant. To quadratic order, this gives \begin{equation} \begin{aligned} - \Sigma(E,\mu^*) + &\Sigma(E,\mu^*) =\mathcal D(\mu^*)+\hat\beta E-\mu r_d+\frac12\left[\hat\beta^2f(1)+(2\hat\beta r_d-d_d)f'(1)+r_d^2f''(1)\right]+\frac12\ln(d_d+r_d^2) \\ - -\frac12\left[ + &-\frac12\left[ \frac12\hat\beta^2\bar c^2f''(0)+(2\hat\beta\bar r-\bar d)\bar cf''(0)+\bar r^2f''(0) -\frac{\bar d^2-2d_d\bar r^2+d_d^2\bar c^2+4r_d\bar r(\bar d+d_d\bar c)-2r_d^2(\bar c\bar d+\bar r^2)}{2(d_d+r_d^2)^2} \right]x_\textrm{max}^2 |