Thermal Simulations, Open Boundary Conditions and Switches
$SU (N)$ gauge theories on compact spaces have a non-trivial vacuum structure characterised by a countable set of topological sectors and their topological charge. In lattice simulations, every topological sector need to be explored a number of times which reflects its weight in the path integral. Current lattice simulations are impeded by the so-called freezing of the topological charge problem. As the continuum is approached, energy barriers between topological sectors become well defined and the simulations get trapped in a given sector. A possible way out was introduced by Luescher using open boundary condition in the time extent. However, this solution cannot be used for thermal simulations, where the time direction is required to be periodic. In this talk, I will present results obtained using open boundary conditions in space, at non-zero temperature. With these conditions, the topological charge is not quantised and the topological barriers are lifted. A downside of this method are the strong finite size effects introduced by the boundary conditions. To conclude, I will present some exploratory results that show how these conditions can be used on an algorithmical level to ”reshuffle” the system and generate periodic configurations with non-zero topological charge.