The complex T -p phase diagram of the van der Waals model around the critical point. The Lee-Yang edges corresponding to T and p are plotted in the 3D complex phase diagram, with an imaginary z-axis of both T and p. The edges converge to the same coexistence line and terminate at the critical point in the physical plane. While in the supercritical region, one witnesses different edges in the complex plane and hence different Widom lines in the physical plane. The inset shows a close connection between the projection of edges and Widom lines.

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... are away from the physical plane, there can be different edges emanating from the same zeros corresponding to different physical properties. As a result, the Widom lines appear at different places. These are exactly the case of phase transition and supercriticality, respectively. An example of complex Tp phase diagram of the vdW model is shown in Fig. 3. The supercritical region is no longer a "no transition's land" since we can see how the complex LY edges determine the phase diagram. The Widom lines largely overlap with the corresponding trajectories of the LY edges, with small deviation due to contributions from non-edge zeros with large density (inset of Fig. 3). In this view, one ...

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... of the vdW model is shown in Fig. 3. The supercritical region is no longer a "no transition's land" since we can see how the complex LY edges determine the phase diagram. The Widom lines largely overlap with the corresponding trajectories of the LY edges, with small deviation due to contributions from non-edge zeros with large density (inset of Fig. 3). In this view, one can interpret supercriticality as a phase transition in the complex phase diagram and an incipient one in the physical phase ...