Yeo Joonhyun, Moore M A
Division of Quantum Phases and Devices, School of Physics, Konkuk University, Seoul 143-701, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 1):052501. doi: 10.1103/PhysRevE.86.052501. Epub 2012 Nov 16.
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 analog 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.
利用Migdal-Kadanoff重整化群近似研究了M-p自旋玻璃模型的两个版本。p = 3且M = 3的模型在平均场水平下，在考兹曼温度处有理想的玻璃化转变，在更低温度下仍有向类似于外场中伊辛自旋玻璃状态的加德纳转变。p = 3且M = 2的模型只有加德纳转变。在所研究的维度d = 2、3和4中，两个模型的行为几乎相同，这表明在这些模型中随着温度降低而增长的关联长度——类似于点到集长度尺度——不是源于玻璃随机一阶转变理论中假定的机制，而是更类似于基于玻璃与外场中伊辛自旋玻璃类比所预期的情况。
