Temperature-reflection symmetry

Abstract

We point out the presence of a $T\ensuremath{\rightarrow}\ensuremath{-}T$ 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.