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arXiv 1208.3044cond-mat.dis-nncond-mat.stat-mech
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M-p-自旋玻璃模型中生长尺度的起源

Origin of the Growing Length Scale in M-p-Spin Glass Models

Joonhyun Yeo, M. A. Moore

摘要:

本文在Migdal-Kadanoff重整化群近似下研究了两种不同形式的M-p-自旋玻璃模型。p=3和M=3的模型具有在平均场水平的理想玻璃转变在Kauzmann温度和在较低的温度下仍然加德纳过渡到一个类似的伊辛自旋玻璃在一个字段中的状态。p=3和M=2的模型只有Gardner跃迁。在研究的尺寸,d= 2,3和4,两个模型的行为几乎相同,这表明在这些模型中,随着温度的降低,相关长度的增长-点到集的长度尺度的模拟-不是由于在玻璃的随机一阶跃迁理论中假设的机制,但更像是在一个领域中的伊辛自旋玻璃的玻璃的模拟所预期的。

英文摘要:

Two versions of the M-p-spin glass model have been studied with the Migdal-Kadanoff renormalization group approximation. The model with p=3 and M=3 has at mean-field level the ideal glass transition at the Kauzmann temperature and at lower temperatures still the Gardner transition to a state like that of an Ising spin glass in a field. The model with p=3 and M=2 has only the Gardner transition. In the dimensions studied, d=2,3 and 4, both models behave almost identically, indicating that the growing correlation length as the temperature is reduced in these models -- the analogue of the point-to-set length scale -- is not due to the mechanism postulated in the random first order transition theory of glasses, but is more like that expected on the analogy of glasses to the Ising spin glass in a field.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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