有限维自旋玻璃中自旋玻璃相的性质

J. Ruiz-Lorenzo
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引用次数: 3

摘要

自旋玻璃是复杂系统的范例。这些材料呈现出非常缓慢的动态。然而,有限维系统中自旋玻璃相的性质仍然存在争议。人们提出了描述低温相的不同理论:液滴、复制对称破缺和混沌对。我们对自旋玻璃的临界性质进行了分析研究,特别是相变处和相变下的临界指数,磁场中相变的存在,下临界维的计算(存在/不存在磁场)。我们还介绍了一些基于转移概念的严谨结果。最后,我们报告了一些关于Aizenman-Wehr亚转移的构建,自旋玻璃相中相关函数的缩放以及场中相变的存在的数值结果,并将这些结果与不同理论的预测进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nature of the Spin Glass Phase in Finite Dimensional (Ising) Spin Glasses
Spin glasses are the paradigm of complex systems. These materials present really slow dynamics. However, the nature of the spin glass phase in finite dimensional systems is still controversial. Different theories describing the low temperature phase have been proposed: droplet, replica symmetry breaking and chaotic pairs. We present analytical studies of critical properties of spin glasses, in particular, critical exponents at and below the phase transition, existence of a phase transition in a magnetic field, computation of the lower critical dimension (in presence/absence of a magnetic field). We also introduce some rigorous results based on the concept of metastate. Finally, we report some numerical results regarding the construction of the Aizenman-Wehr metastate, scaling of the correlation functions in the spin glass phase and existence of a phase transition in a field, confronting these results with the predictions of different theories.
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