Phase transitions due to Euclidean gravity

TL;DR

This paper investigates phase transitions in Euclidean spacetime backgrounds using Ising-like models, revealing that increased curvature induces order-disorder transitions independent of horizons or temperature, and highlights the inhomogeneous nature of these models.

Contribution

It demonstrates that Euclidean gravity's curvature, rather than horizons or temperature, drives phase transitions in inhomogeneous Ising-like models on various geometries.

Findings

Second-order phase transitions occur with increasing curvature.

Rindler geometry does not exhibit a phase transition.

Criticality is not associated with maximal correlation lengths.

Abstract

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.