发表机构
Shanghai Center for Mathematical Sciences and School of Mathematical Sciences, Fudan University（复旦大学数学科学学院上海数学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究具有随机 4 体相互作用的 N 个马约拉纳费米子的 Sachdev--Ye--Kitaev 模型，通过引入新有限浴插值计算每个固定正温度下 SYK 自由能极限，确定施温格 - 戴森压力零温度斜率并转移到谱边缘，得出模型最大特征值相关结论。
AI 中文摘要
我们考虑具有随机 q 体相互作用的 N 个马约拉纳费米子的 Sachdev--Ye--Kitaev 模型。对于 q = 4，我们表明当 N 通过偶数趋于无穷时，该模型的最大特征值几乎必然满足特定等式。证明的主要成分是计算每个固定正温度下 SYK 自由能极限，通过引入新的有限浴插值来实现，将四次 SYK 压力问题简化为在每个此类温度下有效的局部腔核恒等式，然后确定施温格 - 戴森压力的零温度斜率并将其转移到谱边缘。
英文摘要
We introduce a microscopic framework that gives the first rigorous derivation of the Schwinger--Dyson thermodynamics of the Sachdev--Ye--Kitaev model. For fixed, even interaction order $q\geq 4$, we prove that the annealed and quenched normalized pressures converge to the Schwinger--Dyson pressure $p_{{\rm SD},q}(β)$, at any fixed inverse temperature $β>0$. The proof is derived from the finite-$N$ Gibbs state, and it contains three new ingredients: a single-site cavity expansion that keeps the bulk Gibbs state intact, a finite-dimensional locality estimate yielding label-uniform conditional factorization of the Euclidean cavity fields, and an exact Majorana-bath representation of the leading diagrams. We further determine the asymptotic location of the largest eigenvalue, which answers a question posed by Feng--Tian--Wei. Consequently, the sample free-energy density converges almost surely to the zero-temperature value along every sequence $β\equiv β_N\to\infty$.
CommentsStreamlined the argument and modified the title. 49 pages
