Abstract: The thermodynamic interpretation of Schwarzschild black holes has a rich history spanning five decades. In 1973 Bardeen et al. derived the laws of black hole mechanics which suggested a correspondence between (i) temperature and black hole’s mass, specifically T=(8πM)^-1 and (ii) entropy and black hole area: S=A/4. In 1975 Hawking found that a Schwarzschild black hole radiates as if it were a blackbody with temperature T=(8πM)^-1. This meant that the temperature-mass relationship discovered earlier was more than a correspondence. In 1977 Gibbons and Hawking proposed the action of Euclidean Schwarzschild (which also has T=(8πM)^-1) as a means to understand black hole thermodynamics. They recovered S=A/4.  

In this talk we will test if Euclidean Schwarzschild behaves like a heat bath for quantum matter that propagates on it. For simplicity we will use matter with restricted excitations – Ising spins. We will discover that increasing M causes the spins to undergo a second order phase transition from disorder to order and that the phase transition occurs at sub-Planckian M.