6 problems

Let $T_s$ and $T_{sh}$ denote the static and shattering transition temperatures, respectively. For a temperature $T$, say that the free energy landscape is $(E,q,r)$-shattered when…

Let $T_s$ be the static transition temperature, $T_{sh}$ the shattering (dynamical) temperature, and let $T_0$ be the upper endpoint of the interval in which the shattering phase i…

Let $F_{2,N}$ denote the free energy of the spherical SK model with system size $N$, inverse temperature $\beta$, and parameter $J$, and consider the transition between the spin gl…

For a disorder sample, let $\mathbf{u}_1$ be the unit vector corresponding to the ground state, oriented so that $\mathbf{u}_1\cdot\mathbf{g}\geq 0$. Let…

Unlike in the pure $p$-spin model, controlling the free energy sufficiently to obtain information about the cross overlap $|R(\tau^1,\rho^1)|$ is very challenging. Absence of tempe…

Crisanti–Sommers overlap conjecture. The overlap distribution converges to the minimizing measure: for every measurable set $A\subseteq[0,1]$,