Although the physical properties of the 2D and 1D Ising models are quite different, we point out an interesting connection between their complex-temperature phase diagrams. We carry out an exact determination of the complex-temperature phase diagram for the 1D Ising model for arbitrary spin s and show that in the us = e -K s2 plane (i) it consists of Nc,1D = 4s2 infinite regions separated by an equal number of boundary curves where the free energy is nonanalytic; (ii) these curves extend from the origin to complex infinity, and in both limits are oriented along the angles θn = (1 + 2n)π 4s2, for n = 0,...,4s2 - 1; (iii) of these curves, there are Nc,NE,1D = Nc,NW,1D = [s2] in the first and second (NE and NW) quadrants; and (iv) there is a boundary curve (line) along the negative real us axis if and only if s is half-integral. We note a close relation between these results and the number of arcs of zeros protruding into the FM phase in our recent calculation of partition function zeros for the 2D spin s Ising model.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)