外场作用下$p$ -自旋混合模型自由能的涨落
Fluctuations of the free energy in the mixed $p$-spin models with external field
摘要：
我们证明了自旋玻璃混合$p$ -自旋模型中的自由能在外场存在下不超集中，这意味着自由能的方差具有Poincaré不等式所建议的量级.这补充了Chatterjee的结果，Chatterjee表明，当没有外场时，自由能超集中。对于不存在$p\geq 3$的奇$p$ -自旋相互作用的模型，我们证明了任意温度下自由能的中心极限定理，并给出了极限方差的显式表达式。虽然我们只处理了Ising自旋的情况，但我们的结果也可以推广到球模型。
英文摘要：
We show that the free energy in the mixed $p$-spin models of spin glasses does not superconcentrate in the presence of external field, which means that its variance is of the order suggested by the Poincaré inequality. This complements the result of Chatterjee who showed that the free energy superconcentrates when there is no external field. For models without odd $p$-spin interactions for $p\geq 3$, we prove the central limit theorem for the free energy at any temperature and give an explicit formula for the limiting variance. Although we only deal with the case of Ising spins, all our results can be extended to the spherical models as well.
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。
