5 problems

Consider the AKLT state, whose configurations in the Ising basis obey diluted Néel order: between any two $+$ spins there is a $-$ spin and between any two $-$ spins there is a $+$…

Consider an anti-ferromagnetic Potts model on the lattice $\mathbb{Z}^{\Delta}$. Kotecký's long-range-order conjecture. The model exhibits a phenomenon called long-range order. Lon…

The AKLT model is a quantum spin model whose ground states are the lowest-energy states of its Hamiltonian. A state has antiferromagnetic long-range order when spin correlations ex…

Consider a quantum lattice system with a continuous symmetry whose unique ground state exhibits long-range order but no spontaneous symmetry breaking. Suppose that the low-lying ex…

Let the $3$-state antiferromagnetic Potts model be defined on the bipartite lattice $\mathbb{Z}^d$, with configurations assigning one of three states to each vertex and Hamiltonian…