2 problems

Let Skyrmions be topologically protected quasiparticles in a two-dimensional spin lattice, and consider their behavior in the presence of dipolar interactions. Dipole-interaction r…

Let $\rho$ be a Gibbs state of a short-ranged Hamiltonian defined on a $D$-dimensional spin lattice. Let $A$, $B$, and $C$ be three regions, with $B$ shielding $A$ from $C$, and le…