Ensemble equivalence in spin systems with short-range interactions
Ensemble equivalence in spin systems with short-range interactions
复制标题
具有短程相互作用的自旋系统中的系综等价
DOI：
10.1088/1742-5468/2011/08/p08024
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Hidetoshi Nishimori and Victor Martin-Mayor
中科院分区：
文献类型：
--
作者：
Kazutaka Takahasi;Hidetoshi Nishimori and Victor Martin-Mayor
在存在一阶相变的情况下，研究了具有短程相互作用的自旋系统的系综等效问题。对正则系综和微正则系综精确求解了具有非线性近邻相互作用的球面模型。结果表明，在一阶转变点处存在明显的系综不等价性，即微正则熵作为能量的函数是非凹的，因此比热是负的。为了解决这一悖论，我们证明了在代表相分离的微正则计算中应该选择一个非传统的鞍点。用二维微正则蒙特卡罗模拟方法研究了具有非线性相互作用的XY模型，并与球面模型进行了比较。
We study the problem of ensemble equivalence in spin systems with short-range interactions under the existence of a first-order phase transition. The spherical model with nonlinear nearest-neighbour interactions is solved exactly for both canonical and microcanonical ensembles. The result reveals apparent ensemble inequivalence at the first-order transition point in the sense that the microcanonical entropy is non-concave as a function of the energy and consequently the specific heat is negative. In order to resolve the paradox, we show that an unconventional saddle point should be chosen in the microcanonical calculation that represents a phase separation. The XY model with nonlinear interactions is also studied by microcanonical Monte Carlo simulations in two dimensions to see how this model behaves in comparison with the spherical model.