From 8af129d0bda10cb76bf4cf9e7fbcb40febe7d338 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Tue, 29 Oct 2024 10:58:52 +0100 Subject: 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. --- marginal.tex | 4 ++-- 1 file 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. -- cgit v1.2.3-70-g09d2