Abstract

I shall briefly review previous work (due to Yang, Lee, Fisher, and others) that uses the analytic properties of the partition function at complex temperature as a way of categorising and interpreting the behaviour of many-body systems. Such work has traditionally concentrated on calculating the free energies of various classical systems, with a view to analysing their phase transitions. I shall instead ask two questions that do not appear to have been posed before. First, how do the correlation functions of simple magnetic models behave when the temperature becomes complex? Second, how does the analytic structure of the partition function in the complex temperature plane change as a quantum critical point is approached, and what can we learn from those changes? This is very much work in progress (in collaboration with Dr Vadim Oganesyan and Ms Felicitas Beichert), but I shall present a couple of intriguing interim results.