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| author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2024-10-29 10:58:52 +0100 |
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| committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2024-10-29 10:58:52 +0100 |
| commit | 8af129d0bda10cb76bf4cf9e7fbcb40febe7d338 (patch) | |
| tree | 95e73eae7c2da2ec05ac416272ab8f8adf1c9255 | |
| parent | cae62fde30c9da6a91daf478ecd318366d2a9d1a (diff) | |
| download | marginal-8af129d0bda10cb76bf4cf9e7fbcb40febe7d338.tar.gz marginal-8af129d0bda10cb76bf4cf9e7fbcb40febe7d338.tar.bz2 marginal-8af129d0bda10cb76bf4cf9e7fbcb40febe7d338.zip | |
Clarified conditions for decomposition of action
Added language to prevent implying that Gaussianity is sufficient to see
the decomposition of the effective action into two loosly connected
terms.
| -rw-r--r-- | marginal.tex | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/marginal.tex b/marginal.tex index 32f1fd5..cf9db4c 100644 --- a/marginal.tex +++ b/marginal.tex @@ -956,9 +956,9 @@ the contributions from the marginal pieces of the calculation, and is given by \end{equation} \end{widetext} The fact that the complexity can be split into two relatively independent -pieces in this way is a characteristic of the Gaussian nature of the spherical +pieces in this way is a characteristic of the isotropic and Gaussian nature of the spherical spin glass. In Section \ref{sec:least.squares} we will study a model whose -energy is not Gaussian and where such a decomposition is impossible. +energy is isotropic but not Gaussian and where such a decomposition is impossible. There are some dramatic simplifications that emerge from the structure of this particular problem. First, notice that the dependence on the parameters $X$ and $\hat X$ are purely quadratic. |