AI 中文总结
本文针对Sherrington-Kirkpatrick模型，利用Parisi测度的区间支撑，建立了定量Parisi公式，并证明了配分函数方差介于$N^{4/15}$与$N^{7/15}$阶，同时给出自由能和基态能量的偏差界及指数$6/5$的上尾估计。
AI 中文摘要
我们在零外场下建立了Sherrington-Kirkpatrick模型的定量Parisi公式和波动性界。特别地，利用Parisi测度支撑在区间上的事实，我们证明对于任意大于1的固定逆温度，对数配分函数的方差介于$N^{4/15}$和$N^{7/15}$阶之间。相同的指数也适用于基态方差。我们还获得了平均自由能和基态能量的有限尺寸偏差的上下界，以及在正温和零温下指数为$6/5$的双侧上尾估计。
英文摘要
We establish quantitative Parisi formulas and fluctuation bounds for the Sherrington-Kirkpatrick model at zero external field. In particular, using that the Parisi measure is supported on an interval, we show that for every fixed inverse temperature greater than one, the variance of the logarithmic partition function lies between orders $N^{4/15}$ and $N^{7/15}$. The same exponents hold for the ground-state variance. We also obtain upper and lower bounds on the finite-size bias of the mean free energy and ground-state energy, together with two-sided upper-tail estimates with exponent $6/5$ at both positive and zero temperature.
Comments112 pages
