10 problems

Let $G$ be any graph equipped with a ferromagnetic Ising model, with couplings $J_{xy}$, and let $\tau_2$ denote the relaxation time of its Glauber dynamics. Peres's monotonicity c…

Entropy conjecture. The exact location of the multicritical point is given by

Multicritical-point conjecture. The exact location of the multicritical point is determined by $x_0=x_0^{*}$ with $K=K_p$, equivalently

Pressure per particle of the extended Ising model. There exists $\varphi^{\scriptscriptstyle \rm eIsing}(\beta,k,h)$ such that

Let $c=e^{-2\beta H}$ and $d=e^{-2\beta J}$, and consider the one-dimensional 3-permaspin model with couplings $J$ and $H$. Let $z$ be the unique root of the cubic … whose argument…

Constructive automata conjecture. For every context free ${\sf L}_{\mathcal{M}}$ there exists a constructive PDA that decides it. For every context sensitive…

Consider the two-dimensional Ising model on the periodic torus … with nearest-neighbor ferromagnetic coupling $J$, Hamiltonian $\mathcal H_L$, periodic striped configurations…

Let $s$ be a direction and let $\beta_{\rm sat}(s)$ and $\beta_c$ denote the saturation and critical inverse-temperature thresholds, respectively. NSA conjecture. NSA holds for any…

Let $\beta_c$ be the critical inverse temperature, and let ${\bf P}_{\mathbb Z^2,\beta}^{\emptyset}$ denote the infinite-volume sourceless random-current measure on $\mathbb Z^2$.…

Let $\{G_n\}$ be a sequence of transitive graphs, and consider the Glauber dynamics for the Ising model on these graphs. Let $\beta_c$ denote the critical temperature, let $\delta$…