Title: Universality Frontier: Yang-Lee edge singularity

Abstract: Many physical systems have phase transitions terminating at a critical point — below the corresponding temperature, the system separates into two distinct phases (e.g., liquid and vapor). At the critical point,  fluctuations of any scale can occur at a low cost as experimentally manifested by the critical opalescence (milky appearance of a liquid) and theoretically described by the divergent correlation length — the characteristic length scale for fluctuations in the system. Due to the divergent correlations length the dynamics of physical systems at a critical point 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 has not been determined. 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 failed and how our group succeeded in determining the location of the YLE singularity for the most ubiquitous universality classes of critical O(N) theories.

Host: Thomas Schäfer