论文标题
旋转玻璃模型中淬灭压力的第二个衍生物上的上限：弱的griffiths第二不平等
Upper bound on the second derivative of the quenched pressure in spin-glass models: weak Griffiths second inequality
论文作者
论文摘要
格里菲斯第一和第二不平等在铁磁模型的分析中起着重要作用。在旋转玻璃模型中，尽管已经获得了格里菲斯第一不平等的对应物，但格里菲斯的第二不平等现象尚未确定。在这项研究中，我们在先前的工作中概括了该方法[J.物理。 Soc。 JPN。 76，074711（2007）]对相互作用的对称和非对称分布的多变量，并得出了旋转玻璃模型的某些相关性不平等。此外，通过将获得的对称分布中的获得的平等性相结合，我们表明，与随机性强度相对于淬灭压力的第二个导数，在第二个衍生物上有一个非平凡的正上限，这是Griffiths在Spin Glass模型中的第二次不等式的弱结果。
The Griffiths first and second inequalities have played an important role in the analysis of ferromagnetic models. In spin-glass models, although the counterpart of the Griffiths first inequality has been obtained, the counterpart of the Griffiths second inequality has not been established. In this study, we generalize the method in the previous work [J. Phys. Soc. Jpn. 76, 074711 (2007)] to the case with multi variables for both symmetric and non-symmetric distributions of the interactions, and derive some correlation inequalities for spin-glass models. Furthermore, by combining the acquired equalities in symmetric distributions, we show that there is a non-trivial positive upper bound on the second derivative of the quenched pressure with respect to the strength of the randomness, which is a weak result of the counterpart of the Griffiths second inequality in spin-glass models for general symmetric distributions.
