Uniformizing Lee-Yang Singularities

Understand

Motivated by the search for the QCD critical point, we discuss how to obtain the singular behavior of a thermodynamic system near a critical point, namely the Lee-Yang singularities, from a limited amount of local data generated in a different region of the phase diagram.

• We show that by using a limited number of Taylor series coefficients, it is possible to reconstruct the equation of state past the radius of convergence, in particular in the critical region.
• Furthermore we also show that it is possible to extend this reconstruction to go from a crossover region to the first-order transition region in the phase diagram, using a uniformizing map to pass between Riemann sheets.
• We illustrate these ideas via the Chiral Random Matrix Model and the Ising Model.