8 problems

Let $h$ denote the external magnetic field in the Spin $O(N)$ model, where $N$ is an integer, and let the decay constant be the constant in the exponential rate of decay of spin-sp…

Let MCMs be minimally complex models formed as the union of independent irreducible correlation components, and consider spin models with the same number of parameters and the same…

Let $H\colon\Omega\times\Omega\to\mathbb{R}_{\geq 0}$ be a symmetric measurable weighted graph, or model. Call $H$ antiferromagnetic when all eigenvalues other than the top one are…

Let $H\colon\Omega\times\Omega\to\mathbb{R}_{\geq 0}$ be a symmetric measurable weighted graph, or model. Call $H$ clique-maximizing if cliques maximize the relevant homomorphism q…

Let a spin model have finitely many stable and symmetric ground states, and consider the torus $\mathbb T^d_n$. Choose a ground state $\varphi$ uniformly at random from the set…

Let the triangular plaquette model (TPM) be considered at inverse temperature $\beta$. A static and dynamic correlation length is a length scale governing both static and dynamical…

Nonalgebraic-eigenfunction conjecture. Some eigenfunctions of these models are not the ground state times a symmetric function, and their corresponding eigenvalues are not natural…

Let $p$ and $p'$ be the model parameters, let $p_c$ be the critical value, and let $\nu$ be the Bernoulli($p'$) product measure on $\mathcal T$. A local function is a function depe…