关于随机能量模型II关于副本数的解析性：复平面上的零点
On analyticity with respect to the replica number in random energy models II: zeros on the complex plane
摘要：
我们刻画了随机能量模型中通过配分函数矩的复零点对解析性关于副本数的破坏。我们摄动评估的基础上的配分函数利用最速下降法的时刻在过渡点附近的零点，并检查的渐近形式的轨迹的零点系统的大小趋于无穷大。该轨迹的入射角表明解析性破缺类似于二级相变。我们还利用复分析的幅角原理来估计零点的数量。数值计算的有限尺寸系统的实际零点数与分析结果相当吻合。
英文摘要：
We characterize the breaking of analyticity with respect to the replica number which occurs in random energy models via the complex zeros of the moment of the partition function. We perturbatively evaluate the zeros in the vicinity of the transition point based on an exact expression of the moment of the partition function utilizing the steepest descent method, and examine an asymptotic form of the locus of the zeros as the system size tends to infinity. The incident angle of this locus indicates that analyticity breaking is analogous to a phase transition of the second order. We also evaluate the number of zeros utilizing the argument principle of complex analysis. The actual number of zeros calculated numerically for systems of finite size agrees fairly well with the analytical results.
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