Rodríguez-Camargo C D, Mojica-Nava E A, Svaiter N F
Centro de Estudios Industriales y Logísticos para la productividad (CEIL, MD), Programa de Ingeniería Industrial, Corporación Universitaria Minuto de Dios, Bogotá AA 111021, Colombia.
Programa de Investigación sobre Adquisición y Análisis de Señales (PAAS-UN), Universidad Nacional de Colombia, Bogotá AA 055051, Colombia.
Phys Rev E. 2021 Sep;104(3-1):034102. doi: 10.1103/PhysRevE.104.034102.
We discuss the Sherrington-Kirkpatrick mean-field version of a spin glass within the distributional zeta function method (DZFM). In the DZFM, since the dominant contribution to the average free energy is written as a series of moments of the partition function of the model, the spin-glass multivalley structure is obtained. Also, an exact expression for the saddle points corresponding to each valley and a global critical temperature showing the existence of many stables or at least metastable equilibrium states is presented. Near the critical point, we obtain analytical expressions of the order parameters that are in agreement with phenomenological results. We evaluate the linear and nonlinear susceptibility and we find the expected singular behavior at the spin-glass critical temperature. Furthermore, we obtain a positive definite expression for the entropy and we show that ground-state entropy tends to zero as the temperature goes to zero. We show that our solution is stable for each term in the expansion. Finally, we analyze the behavior of the overlap distribution, where we find a general expression for each moment of the partition function.
我们在分布zeta函数方法（DZFM）内讨论自旋玻璃的谢林顿 - 柯克帕特里克平均场版本。在DZFM中，由于对平均自由能的主要贡献被写为模型配分函数的一系列矩，所以获得了自旋玻璃多谷结构。此外，还给出了对应于每个谷的鞍点的精确表达式以及一个全局临界温度，该临界温度表明存在许多稳定或至少亚稳平衡态。在临界点附近，我们得到了与唯象结果一致的序参量的解析表达式。我们评估了线性和非线性磁化率，并发现了自旋玻璃临界温度处预期的奇异行为。此外，我们得到了熵的正定表达式，并表明随着温度趋于零，基态熵趋于零。我们表明我们的解对于展开式中的每一项都是稳定的。最后，我们分析了重叠分布的行为，在此我们找到了配分函数每个矩的一般表达式。
