4 problems

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The equilibrium fluctuation threshold conjecture for the weakly perturbed interface model
Let $\mathcal{Q}^N$ be the law on $D([0,T],\mathcal{S}'(\mathbb{T}))$ of the fluctuation field $\{\mathscr{U}^N_t,t\in[0,T]\}_N$ , with $N=2p$ for $p$ prime. For the stationary solu…
Conjectureopenhydrodynamic-limits random-interfaces stochastic-processesarXiv posted 2 days ago
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The roughening transition conjecture for the 3D Ising model
Consider the three-dimensional Ising model at inverse temperature $\beta>\beta_c$ , with a horizontal interface in a box of horizontal size $n$ . Long-range order refers to persisten…
Conjectureopenising-model random-interfaces rougheningarXiv posted 2 days ago
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Conjecture that rigidity fails near criticality or under tilt in the 3D Ising model
Let $\beta>\beta_c$ be the inverse temperature of the Ising model, and consider the low-temperature interface in dimension $d=3$ , either near the critical inverse temperature…
Conjectureopenising-model random-interfaces rougheningarXiv posted 2 days ago
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Caravenna–Bolthausen conjecture on the free energy of the pinned one-dimensional $(\nabla+\Delta)$ -model
Consider the one-dimensional mixed $(\nabla+\Delta)$ -model with pinning, interpolating between the discrete Gaussian free field at $\kappa_2=0$ and the pure Laplacian interaction m…
Conjectureopenfree-energy random-interfaces statistical-mechanicsarXiv posted 2 days ago

4 problems

The equilibrium fluctuation threshold conjecture for the weakly perturbed interface model

The roughening transition conjecture for the 3D Ising model

Conjecture that rigidity fails near criticality or under tilt in the 3D Ising model

Caravenna–Bolthausen conjecture on the free energy of the pinned one-dimensional (∇+Δ)(\nabla+\Delta)(∇+Δ)-model

Caravenna–Bolthausen conjecture on the free energy of the pinned one-dimensional $(\nabla+\Delta)$ -model