Lee-Yang and Langer edge singularities from analytic continuation of scaling functions

Abstract

We discuss the analytic continuation of scaling function in the 3-dimensional Z(2),O(2) andO(4) universality classes using the Schofield representation of the magnetic equation of state. We show that a determination of the location of Lee-Yang edge singularities and, in the case of Z(2), also the Langer edge singularity yields stable results. Results for the former are in good agreement with Functional Renormalization Group calculations. We also present results for the location of the Langer edge singularity in the 3-d,Z(2) universality class. We find that in terms of the complex scaling variable z the distance of the Langer edge singularity to the critical point agrees within errors with that of the Lee-Yang edge singularity. Furthermore the magnitude of the discontinuity along the Langer branch cut is an order of magnitude smaller than that along the Lee-Yang branch cut.

13 pages, 6 figures, matches published version

References in corpus (8)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• 50 Years of Quantum Chromodynamics
• Monte Carlo study of an improved clock model in three dimensions
• Taylor expansions and Padé approximants for cumulants of conserved charge fluctuations at non-vanishing chemical potentials
• Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density
• Uniformizing Lee-Yang Singularities
• Determination of Lee-Yang edge singularities in QCD by rational approximations
• Scaling functions of the three-dimensional $Z(2)$, $O(2)$ and $O(4)$ models and their finite size dependence in an external field

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