Two lectures on Yang-Lee edge singularity and analytic structure of QCD equation of state

Abstract

These lecture notes, prepared for the 2024 XQCD PhD, provide an introduction to the analytic structure of an equation of state near a second-order phase transition and its most prominent landmark: the Yang-Lee edge singularity. In addition to discussing general properties, the notes review recent theoretical progress in locating the QCD critical point by tracking the trajectory of the Yang-Lee edge singularity.

37 pages, 19 figures

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• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• The QCD phase diagram for small densities from imaginary chemical potential
• The nonperturbative functional renormalization group and its applications
• The QCD phase structure at finite temperature and density
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Nonperturbative renormalization group approach to frustrated magnets
• Meson fluctuations and thermodynamics of the Polyakov loop extended quark-meson model
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• Ising exponents from the functional renormalisation group
• Derivative expansion and renormalisation group flows
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• Repulsive baryonic interactions and lattice QCD observables at imaginary chemical potential
• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• Baryon number fluctuations in the QCD phase diagram from Dyson-Schwinger equations
• Fixed Points Structure & Effective Fractional Dimension for O(N) Models with Long-Range Interactions
• QCD Critical Point and Complex Chemical Potential Singularities
• Solutions of renormalization group flow equations with full momentum dependence
• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• Renormalization Group Flow Equations and the Phase Transition in O(N)-models
• Critical exponents of O(N) models in fractional dimensions
• The scaling functions of the free energy density and its derivatives for the 3d O(4) model
• Order parameters and color-flavor center symmetry in QCD
• High-accuracy scaling exponents in the local potential approximation
• Roberge-Weiss endpoint at the physical point of $N_f=2+1$ QCD
• Universal location of the Yang-Lee edge singularity in O(N) theories
• The Functional Renormalization Group and O(4) scaling
• Global Wilson-Fisher fixed points
• Critical O(N) models above four dimensions: Small-N solutions and stability
• New approach to canonical partition functions computation in $N_f=2$ lattice QCD at finite baryon density
• Critical $O(N)$ models in the complex field plane
• 2D Ising Field Theory in a Magnetic Field: The Yang-Lee Singularity
• Why Might the Standard Large $N$ Analysis Fail in the O($N$) Model: The Role of Cusps in the Fixed Point Potentials
• Scaling functions for the O(4)-model in d=3 dimensions
• Finite-Size Scaling behavior in the O(4)-Model
• Functional renormalization group approach to the Yang-Lee edge singularity
• On spinodal points and Lee-Yang edge singularities
• Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}({\partial }^4)$
• Universal location of Yang-Lee edge singularity for a one-component field theory in $1\le d\le 4$
• Universal location of Yang-Lee edge singularity in classic O(N) universality classes
• Fourier coefficients of the net-baryon number density and chiral criticality
• Critical $O(2)$ field theory near six dimensions beyond one loop
• Universal scaling and the asymptotic behaviour of Fourier coefficients of the baryon-number density in QCD
• Searching for the QCD critical endpoint using multi-point Padé approximations

Cited by in corpus (1)

• Lattice-based equation of state with a critical point from constant entropy contours and its comparison to effective QCD approaches