From 8af129d0bda10cb76bf4cf9e7fbcb40febe7d338 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
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(-)

(limited to 'marginal.tex')

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

