F. Beichert, C. A. Hooley, R. Moessner, V. Oganesyan
We investigate the spin-spin correlation functions of Ising magnets at complex values of the temperature, T. For one-dimensional chain and ladder systems, we show the existence of a kind of helimagnetic order in the vicinity of contours where the leading two eigenvalues of the transfer matrix become equal in magnitude. We analyse the development of long-range order as the two-dimensional limit is approached, and find that there is rich structure in much of the complex-T plane. In particular, and contrary to the work of Fisher on this problem, the development of long-range order is actually associated with a proliferation of partition function zeros in a certain finite region of that plane containing the real-temperature magnetically ordered phase. The thermodynamic consequences of this are also discussed.
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http://arxiv.org/abs/1304.6314
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