Limitations of entanglement entropy in detecting thermal phase transitions

We explore the efficacy of entanglement entropy as a tool for detecting thermal phase transitions in a family of gauge theories described holographically. The rich phase diagram of these theories encompasses first and second-order phase transitions, as well as a critical and a triple point. While entanglement measures demonstrate some success in probing transitions between plasma phases, they prove inadequate when applied to phase transitions leading to gapped phases. Nonetheless, entanglement measures excel in accurately determining the critical exponent associated with the observed phase transitions, providing valuable insight into the critical behavior of these systems.