From 2a2a4e5d4b3b700ce27e7f948e6ab6f61e18693b Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Mon, 10 Mar 2025 14:47:35 -0300 Subject: Change addressing report #2, second question Added a footnote discussing the comparison between our prediction of V_SAT and that made in the confluent tissues paper. --- topology.tex | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) (limited to 'topology.tex') diff --git a/topology.tex b/topology.tex index 99c9a06..d3d90d4 100644 --- a/topology.tex +++ b/topology.tex @@ -409,7 +409,9 @@ $V_0=V_\text{\textsc{sat}}$ corresponding to the vanishing of the effective action at the $m=0$ solution, with $\mathcal S(0)=0$. For a generic covariance function $f$ it is not possible to write an explicit formula for $V_\text{\textsc{sat}}$, and we calculate it through a numeric -root-finding algorithm. +root-finding algorithm.\footnote{ +As a check of this calculation, the satisfiability threshold calculated here can be compared with that calculated using the zero-temperature limit of an equilibrium treatment of the cost function \eqref{eq:cost} made in Ref.~\cite{Urbani_2023_A} for the case where $f(q)=\frac12q^2$ and $\alpha=\frac14$. The authors estimate $V_\text{\textsc{sat}}\simeq1.871$, whereas this manuscript predicts $V_\text{\textsc{sat}}=1.867229\dots$, a seeming inconsistency. However, the author of Ref.~\cite{Urbani_2023_A} indicated in private correspondence that this difference could easily be explained by inaccuracy in the numeric \textsc{pde} treatment of the \textsc{frsb} equilibrium problem. Therefore, this manuscript is consistent with the previous work, but the agreement is not precise. +} When $V_0^2