On the symmetry of a Preisach map
  At the very heart of the successful phenomenological model of magnetic hysteresis there is the so called Preisach distribution. In the existing literature it is implicitly assumed, that this distribution has a mirror symmetry. We show, by simple and convincing example, that this common assumption is plainly wrong. Dropping it, we gain the ability to model not only the usual hysteresis loops (major and minor) more accurately than ever before, but also those displaying the exchange bias effect, what is impossible within the framework of the symmetrical Preisach model. It is hoped, that our observation paves the way towards the unified description of all the hysteretic systems, including, but not necessarily limited to, superconductors, (multi)layered structures, nanocrystalline materials, patterned media, and - perhaps - the other non-magnetic hysteretic phenomena. 
Marek W. Gutowski