Exploring the Phase Diagram with Taylor Series: Epic Voyage or Just Another Bad Trip

TL;DR

This paper investigates the effectiveness of Taylor series expansions in locating critical points in phase diagrams, using the 3D Ising model as a test case to validate the method for QCD studies.

Contribution

It demonstrates that Taylor coefficients can successfully identify the critical point in the Ising model, supporting their use in QCD phase diagram exploration.

Findings

Taylor coefficients pinpoint the Ising critical point

Method validates the use of Taylor series for phase transition detection

Supports application to QCD critical point search

Abstract

It has been suggested in the literature that it may be possible to locate the QCD critical end point using the Taylor series of thermodynamic variables about the $\mu=0$ axis. Since the phase transition at the critical end point is believed to be in the 3D Ising universality class, it would seem natural to test this method with the Ising Model, for which the answer is already known. The finding is that it is in fact possible to pinpoint the location of the Ising critical point using Taylor coefficients.