The Griffiths inequalities for Ising spin glasses are proved on the Nishimori line with various bond randomness which includes Gaussian and $\pm J$ bond randomness. The proof for Ising systems with Gaussian bond randomness has already been carried out by Morita et al, which uses not only the gauge theory but also the properties of the Gaussian distribution, so that it cannot be directly applied to the systems with other bond randomness. The present proof essentially uses only the gauge theory, so that it does not depend on the detail properties of the probability distribution of random interactions. Thus, the results obtained from the inequalities for Ising systems with Gaussian bond randomness do also hold for those with various bond randomness, especially with $\pm J$ bond randomness.
Griffiths inequalities and Gibbs-Bogoliubov inequality for general gauge glasses with Gaussian disorder on Nishimori line
Graduate School of Information Sciences, Tohoku University（东北大学信息科学研究院）；School of Computing, Institute of Science Tokyo（东京科学大学理工学院）；Department of Physics, Institute of Science Tokyo（东京科学大学物理系）；Research and Education Institute for Semiconductors and Informatics, Kumamoto University（熊本大学半导体与信息教研院）；Sigma-i Co., Ltd.（Sigma-i有限公司）
Existence of a Phase Transition in the One-Dimensional Ising Spin Glass Model with Long-Range Interactions on the Nishimori Line
Graduate School of Information Sciences, Tohoku University（东北大学情报科学研究院）；School of Computing, Institute of Science Tokyo（东京科学大学理工学院）；Department of Physics, Institute of Science Tokyo（东京科学大学物理系）；Research and Education Institute for Semiconductors and Informatics, Kumamoto University（熊本大学半导体与信息学研究与教育学院）；Sigma-i Co., Ltd.（Sigma-i有限公司）
Specific heat and non-linear susceptibility in spin glasses with random fields
基于LiHo $_x$ Y $_{1-x}$ F $_4$在弱横场作用下产生无规场的假设，研究了自旋玻璃SG体系在无规场作用下的磁性.我们考虑了一个团簇自旋模型，它允许团簇之间的长程无序相互作用和团簇内部的短程相互作用，除了一个本地RF为每个自旋以下的高斯分布与标准偏差$Δ$。我们采用一步复制对称破缺（RSB）方法得到一个精确可解的单簇问题。讨论了不同无序组态的序参量、比热$C_{m}$、非线性极化率$χ_3$和相图的行为。在没有RF的情况下，$χ_3$在$T_f$处表现出发散，而$C_{m}$在比$T_f$高约30 $\%$的温度$T^{**}$处显示出宽的最大值，如对于常规SG系统所预期的。RF的出现改变了这种情况。$C_{m}$仍在$T^{**}$处显示最大值，其对$Δ$的依赖性较弱。然而，$T_f$被置换到较低的温度，显著提高了$T^{**}/T_f$的比率。此外，$χ_3$中的发散被在温度$T^{*}$下的四舍五入的最大值所取代，随着$Δ$的增强，该温度变得越来越高于$T_f$。因此，顺磁相在三个区域展开：（i）常规顺磁性（$T>T^{**}$）;（ii）具有冻结自旋的短程有序形成的区域（$T^{*}<T<T^{**}$）;（iii）具有在SG转变之前减慢自旋动力学的自由能势垒缓慢增长的区域（$T_f<T<T^{*}$），这表明在SG状态之前存在中间格里菲斯相。我们的研究…
Exact mapping of a spin glass with correlated disorder to the pure Ising model
Institute of Integrated Research, Institute of Science Tokyo（东京科学大学综合研究学院）；Graduate School of Information Sciences, Tohoku University（东北大学情报科学研究院）；RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所交叉理论数学科学中心（iTHEMS））
