| Abstract: | Topological phases of matter are one of the hallmarks for quantum condensed matter physics. Still, it turns out that many of them have exact mathematical analogues which are purely classical. In this talk, I'll describe one such classical analogue -- the classical topological paramagnet. In addition I'll discuss how having a quantized thermal conductance prohibits the construction of such classical analogues. A different way to phrase this is that having a nonzero quantized thermal conductance makes it impossible to solve the sign problem in quantum Monte Carlo simulations. |