3 problems

Let $\beta_c^Q$ denote the quenched critical value for adsorption, and let the models be lattice trees and lattice animals in dimension $d$. Finite critical value conjecture. The q…

Let $\beta_c^Q(\mathcal{P}^X)$ denote the quenched critical value for the model $\mathcal{P}^X$, with $\mathcal{T}^{\circ \! |\! \circ}$ and $\mathcal{T}^+$ the penetrable and impe…

Let $\beta_c$ denote the critical interaction parameter separating the extended and collapsed regimes, and let ${{\mathcal E}}$ be the extended phase. Critical-curve conjecture. Th…