Ensemble inequivalence in the ferromagneticp-spin model in random fields

Abstract

We study the effect that randomness has on long-range interacting systems by using the ferromagnetic Isingmodel with p-body interactions in random fields. The case withp = 2 yields a phase diagram similar to that of previously studied models and shows knownfeatures that the inequivalence of the canonical and microcanonical ensembles brings withit, for example negative specific heat in a narrow region of the phase diagram. Whenp > 2, however, the canonical phase diagram is completely different from the microcanonical one.The temperature does not necessarily determine the microcanonical phases uniquely, andthus the ferromagnetic and paramagnetic phases are not separated in such aregion of a conventional phase diagram drawn with the temperature and fieldstrength as the axes. Below a certain value of the external field strength, partof the ferromagnetic phase has negative specific heat. For large values of theexternal field strength the ergodicity is broken before the phase transition occurs forp > 2. Moreover,for p > 2, the Maxwell construction cannot be derived in a consistent manner and therefore, incontrast to previous cases with negative specific heat, the Maxwell construction does notbridge the gap between the ensembles.