Phase transitions at finite density

TL;DR

This paper analyzes the complex analytic structure of thermodynamic quantities near phase transitions, introducing a conformal mapping technique to improve the study of strongly interacting matter at finite baryon density.

Contribution

It presents a novel conformal mapping method to explore phase transitions at finite density using lattice QCD data, enhancing the analysis of singularities in the complex chemical potential plane.

Findings

Conformal mapping improves convergence of Taylor expansions around μ=0.

Method enhances sensitivity to phase transition singularities.

Application to a chiral model demonstrates effectiveness.

Abstract

I discuss the analytic structure of thermodynamic quantities for complex values of thermodynamic variables within Landau theory. In particular, the singularities connected with phase transitions of second order, first order and cross over types are examined. A conformal mapping is introduced, which may be used to explore the thermodynamics of strongly interacting matter at finite values of the baryon chemical potential $\mu$ starting from lattice QCD results at $\mu^{2}\leq 0$. This method allows us to improve the convergence of a Taylor expansion about $\mu=0$ and to enhance the sensitivity to physical singularities in the complex $\mu$ plane. The technique is illustrated by an application to a second-order transition in a chiral effective model.