低温Sherrington–Kirkpatrick自由能的极限律
The low-temperature Sherrington–Kirkpatrick free-energy limiting law
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具体内容
稿件研究零场Gaussian Ising Sherrington–Kirkpatrick模型的自由能涨落。作者声称：对每个固定逆温度β>1，当系统规模沿所有整数趋于无穷时，自由能减去其期望再除以其标准差，依分布收敛到非退化极限律；并证明其方差除以n^{1/3}收敛到有限正常数。该结果刻画低温自旋玻璃自由能的精细涨落尺度，属概率论与统计物理交叉研究。
- 作者声称对每个固定β>1，中心化标准化自由能依分布收敛到非退化律
- 证明自由能方差除以n^{1/3}收敛到有限正常数
- 研究对象为零场Gaussian Ising SK模型
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英文原始摘要
For every fixed inverse temperature β > 1, we prove that the zero-field Gaussian Ising Sherrington–Kirkpatrick free energy, centered by its expectation and divided by its standard deviation, converges in distribution to a nondegenerate law as the system size tends to infinity through all integers. We also prove that its variance divided by n1/3 converges to a finite positive constant.
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