Phase transitions due to Euclidean gravity

We use Ising-like models to probe the thermal nature of Euclidean spacetime backgrounds. We determine which properties of the background -- curvature, the presence of a horizon, or temperature -- play a role in phase transitions. The geometries we use are Euclidean Schwarzschild, Rindler, extremal Reissner-N\"{o}rdstrom (ERN), Anti deSitter (AdS), and deSitter (dS). Among these, Rindler is flat, AdS does not have a horizon, and both AdS and ERN have zero temperatures. We find second-order phase transitions as the metric parameter is varied in all cases except for Rindler. Specifically, we find that the transition from order to disorder occurs as the curvature -- or Euclidean gravity -- increases. This supports our conjecture that Euclidean gravity is an essential ingredient for these phase transitions, as opposed to the presence of a horizon or temperature. Separately, since the selected geometries are position-dependent, the Ising-like models constructed on them are inhomogeneous, whereby they generalize the standard Ising model. We find that a consequence of this is that criticality does not correspond to maximal correlation lengths and scale invariance.