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| -rw-r--r-- | frsb_kac-rice_letter.tex | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/frsb_kac-rice_letter.tex b/frsb_kac-rice_letter.tex index 84d708d..63b7811 100644 --- a/frsb_kac-rice_letter.tex +++ b/frsb_kac-rice_letter.tex @@ -27,7 +27,7 @@ \begin{abstract} Complexity is a measure of the number of stationary points in complex - landscapes. We derive a general solution for the complexity of mean-field + landscapes. We {\color{red} solve the long-standing problem of detremining the...} derive a general solution for the complexity of mean-field complex landscapes. It incorporates Parisi's solution for the ground state, as it should. Using this solution, we count the stationary points of two models: one with multi-step replica symmetry breaking, and one with full @@ -95,8 +95,8 @@ models have $a_p=1$ for some $p$ and all others zero. The complexity of the $p$-spin models has been extensively studied by physicists and mathematicians. Among physicists, the bulk of work has been on -the so-called Thouless--Anderson--Palmer (TAP) complexity for the pure models, -which counts minima in a kind of mean-field free energy \cite{Rieger_1992_The, + the so-called `TAP' complexity, +which counts minima in the mean-field Thouless--Anderson--Palmer () free energy \cite{Rieger_1992_The, Crisanti_1995_Thouless-Anderson-Palmer, Cavagna_1997_An, Cavagna_1997_Structure, Cavagna_1998_Stationary, Cavagna_2005_Cavity, Giardina_2005_Supersymmetry}. The landscape complexity has been proven for pure @@ -165,7 +165,7 @@ population of stationary points suddenly shifts from all saddles to all minima, and there is an abrupt percolation transition in the topology of constant-energy slices of the landscape. This behavior of the complexity can be used to explain a rich variety of phenomena in the equilibrium and dynamics of -the pure models: the threshold energy $E_\mathrm{th}$ corresponds to the +the pure models: the `threshold' \cite{Cugliandolo_1993_Analytical} energy $E_\mathrm{th}$ corresponds to the average energy at the dynamic transition temperature, and the asymptotic energy reached by slow aging dynamics. |