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International Journal of Theoretical Physics

Microcanonical Analysis on a System with Long-Range Interactions

Ji-Xuan Hou, Xu-Chen Yu, Jing-Min Hou

Published Apr 23, 2016• 18 citations
Publisher
DOI
10.1007/s10773-016-3021-z

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Ensemble inequivalence, where a system's thermodynamic properties depend on the statistical ensemble used to describe it, is a well-established phenomenon in classical systems with long-range interactions. Here, we present a detailed analysis of a quantum ferromagnet spin model that exhibits this same behavior. We find that the microcanonical and canonical phase diagrams are identical at zero temperature ( T = 0 ), but differ significantly at finite temperatures. Our results highlight a breakdown of ensemble equivalence in this quantum long-range model, contrasting with what is observed for short range. These findings have important implications for the study and manipulation of long-range interacting quantum platforms, such as those used in atomic, molecular, and optical physics.
The thermodynamic and dynamical properties of an Ising model with both short-range and long-range, mean-field-like, interactions are studied within the microcanonical ensemble. It is found that the relaxation time of thermodynamically unstable states diverges logarithmically with system size. This is in contrast with the case of short-range interactions where this time is finite. Moreover, at sufficiently low energies, gaps in the magnetization interval may develop to which no microscopic configuration corresponds. As a result, in local microcanonical dynamics the system cannot move across the gap, leading to breaking of ergodicity even in finite systems. These are general features of systems with long-range interactions and are expected to be valid even when the interaction is slowly decaying with distance.
A long-range interacting Fermi chain placed in the uniform and the staggered magnetic field is studied via the micro-canonical approach. The relation between the entropy and the energy of the system is obtained by counting the number of microscopic states. We find that this system is non-ergodic and can exhibit first-order phase transition, second-order phase transition, or both. The microcanonical ensemble predicts negative specific heat regions and temperature jumps. Moreover, the global phase diagram of the system is constructed.