Frontier of Universality: Yang-Lee edge singularity

At the critical point,  fluctuations of any scale can occur at a low cost as experimentally manifested by the critical opalescence and theoretically described by the divergent correlation length. Owing to this divergence the dynamics of physical systems become independent of potentially radically diverse microscopic structures and is only defined by a few macroscopic properties – dimensionality and global symmetries. This striking reduction allows categorizing the systems into just a few universality classes, with the members of the same class having identical critical behavior. The critical exponents and amplitudes, the most well-known universal quantities, are encoded in the asymptotic behavior of a universal function – the critical equation of state. More than a century of dedicated research revealed numerous features of the critical equations of state to unprecedented precision for many universality classes. There is one notable exception: the location of the Yang-Lee Edge (YLE) singularity, which has not been determined until recently. I will introduce the notion of the YLE  singularity and explain why knowing its location is important. Next, I will discuss why the conventional techniques fail and tell you which approach can be used to determine the location of the singularity for the most ubiquitous universality classes of critical O(N) theories.