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Thermodynamic limits from excited quantum phase transitions via exceptional point trajectory calculations.
Here we show for the Lipkin model that as the number of interacting particles are increased the exceptional points associated with ground and excited state quantum phase transitions are accumulated along the real order parameter axis. Using the Pad´e approximant we obtain the thermodynamic limit of the phase transition. The key point in our approach is the use of the fact that for finite systems critical phenomena are uniquely defined only within the framework of nonhermitian quantum mechanics where exceptional points in the spectra are obtained. This approach can be used for studying phase transition in other systems where due to the interaction of practically infinite large number of molecules a thermodynamical phase transition occurs.