Temperature-reflection symmetry

We point out the presence of a T→-T temperature-reflection (T-reflection) symmetry for the partition functions of many physical systems. Without knowledge of the origin of the symmetry, we have only been able to test the existence of T-reflection symmetry in systems with exactly calculable partition functions. We show that T-reflection symmetry is present in a variety of conformal and nonconformal field theories and statistical mechanics models with known partition functions. For example, all minimal model partition functions in two-dimensional conformal field theories are invariant under T-reflections. An interesting property of the T-reflection symmetry is that it can be broken by shifts of the vacuum energy.