2011/01/14 by Zsolt Bertalan, Takehiro Kuma, Yoshiki Matsuda +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Canonical ensemble #Complex Systems and Time Series Analysis #Condensed matter physics #Ergodicity #Ferromagnetism #Ising model #Mathematics #Microcanonical ensemble #Monte Carlo method #Phase (matter) #Phase diagram #Phase transition #Physics #Quantum mechanics #Randomness #Statistical Mechanics and Entropy #Statistics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2011/01/p01016
published as J. Stat. Mech. (2011) P01016
openalex publication_date 2011/01/14 · arxiv created 2011/01/21 · arxiv updated 2015/03/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the effect that randomness has on long-range interacting systems by using the ferromagnetic Ising model with p -body interactions in random fields. The case with p = 2 yields a phase diagram similar to that of previously studied models and shows known features that the inequivalence of the canonical and microcanonical ensembles brings with it, for example negative specific heat in a narrow region of the phase diagram. When p > 2, however, the canonical phase diagram is completely different from the microcanonical one. The temperature does not necessarily determine the microcanonical phases uniquely, and thus the ferromagnetic and paramagnetic phases are not separated in such a region of a conventional phase diagram drawn with the temperature and field strength as the axes. Below a certain value of the external field strength, part of the ferromagnetic phase has negative specific heat. For large values of the external field strength the ergodicity is broken before the phase transition occurs for p > 2. Moreover, for p > 2, the Maxwell construction cannot be derived in a consistent manner and therefore, in contrast to previous cases with negative specific heat, the Maxwell construction does not bridge the gap between the ensembles.