Fronczak Agata, Fronczak Piotr, Siudem Grzegorz
Faculty of Physics, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland.
Phys Rev E. 2020 Feb;101(2-1):022111. doi: 10.1103/PhysRevE.101.022111.
In this paper, we draw attention to the problem of phase transitions in systems with locally affine microcanonical entropy, in which partial equivalence of (microcanonical and canonical) ensembles is observed. We focus on a very simple spin model, that was shown to be an equilibrium statistical mechanics representation of the biased random walk. The model exhibits interesting discontinuous phase transitions that are simultaneously observed in the microcanonical, canonical, and grand canonical ensemble, although in each of these ensembles the transition occurs in a slightly different way. The differences are related to fluctuations accompanying the discontinuous change of the number of positive spins. In the microcanonical ensemble, there is no fluctuation at all. In the canonical ensemble, one observes power-law fluctuations, which are, however, size dependent and disappear in the thermodynamic limit. Finally, in the grand canonical ensemble, the discontinuous transition is of mixed order (hybrid) kind with diverging (critical-like) fluctuations. In general, this paper consists of many small results, which together make up an interesting example of phase transitions that are not covered by the known classifications of these phenomena.
在本文中，我们关注具有局部仿射微正则熵的系统中的相变问题，在这类系统中观察到了（微正则和正则）系综的部分等价性。我们聚焦于一个非常简单的自旋模型，该模型已被证明是有偏随机游走的平衡统计力学表示。该模型展现出有趣的不连续相变，这种相变在微正则、正则和巨正则系综中同时被观察到，尽管在这些系综中的每一个中相变以略有不同的方式发生。这些差异与正自旋数的不连续变化所伴随的涨落有关。在微正则系综中，根本不存在涨落。在正则系综中，人们观察到幂律涨落，然而，这种涨落依赖于系统大小，并且在热力学极限下消失。最后，在巨正则系综中，不连续相变是混合阶（混合）类型，具有发散（类临界）涨落。总体而言，本文由许多小结果组成，这些结果共同构成了一个有趣的相变例子，是已知这些现象分类未涵盖的。
