Topological behavior in a solvable 3D model

Recently, arxiv:2202.11303 discovered a solvable classical 3D model that has topological behavior, with loop observables -- products of spins on loops -- that depend on only their topology. Specifically, averages of non-contractible loops vanish while contractible loops average to one. However, because the model is solvable only at special points, the robustness of these observations has remained unknown. In this talk, I will show that the loop observables are robust to perturbations over ranges of temperatures and loop sizes that are large when the perturbation is small. I will present arguments for these claims, and show quantitative evidence using numerically exact calculations using Monte Carlo methods, with custom Monte Carlo moves to ensure ergodic sampling of configurations.