Lee-Yang theory, complex phase diagram, and supercritical matter

The supercritical region is often described as uniform with no definite transitions.The distinct behaviors of the matter therein, e.g., as liquid-like and gas-like, however, indicate their should-be different belongings. Here, we provide a mathematical description of these phenomena by revisiting the Lee-Yang (LY) theory and using a complex phase diagram, e.g. a 4-D one with complex T and p. Beyond the critical point, the 2-D phase diagram with real T and p, i.e. the physical plane, is free of LY zeros and hence no criticality emerges. But off-plane zeros in this 4-D scenario still come into play by inducing critical anomalies for different physical properties. This is evidenced by the correlation between the Widom line and LY edges in van der Waals model and water. The present distinct criteria to distinguish the supercritical matter manifest the high-dimensional feature of the phase diagram: e.g. when the LY zeros of complex T or p are projected onto the physical plane, a boundary defined by isobaric heat capacity Cp or adiabatic compression coefficient K_T emanates. These results demonstrate the incipient phase transition nature of the supercritical matter.