Quenched vs Annealed: Glassiness from SK to SYK

C. Baldwin, C. Baldwin, Brian Swingle
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引用次数: 18

Abstract

We show that any SYK-like model with finite-body interactions among \textit{local} degrees of freedom, e.g., bosons or spins, has a fundamental difference from the standard fermionic model: the former fails to be described by an annealed free energy at low temperature. In this respect, such models more closely resemble spin glasses. We demonstrate this by two means: first, a general theorem proving that the annealed free energy is divergent at low temperature in any model with a tensor product Hilbert space; and second, a replica treatment of two prominent examples which exhibit phase transitions from an "annealed" phase to a "non-annealed" phase as a function of temperature. We further show that this effect appears only at $O(N)$'th order in a $1/N$ expansion, even though lower-order terms misleadingly seem to converge. Our results prove that the non-bosonic nature of the particles in SYK is an essential ingredient for its physics, highlight connections between local models and spin glasses, and raise important questions as to the role of fermions and/or glassiness in holography.
淬火与退火:从SK到SYK的玻璃性
我们证明了任何具有\textit{局部}自由度之间有限体相互作用的syk类模型,例如玻色子或自旋,与标准费米子模型有一个根本的区别:前者不能用低温下的退火自由能来描述。在这方面,这些模型更接近于旋转眼镜。我们用两种方法证明了这一点:首先,证明了在具有张量积Hilbert空间的任何模型中,退火自由能在低温下发散的一般定理;其次,对两个突出的例子进行了复制处理,这两个例子显示了从“退火”相到“非退火”相的相变作为温度的函数。我们进一步表明,这种效应只出现在$1/N$展开的$O(N)$ ' s阶,即使低阶项似乎错误地收敛。我们的结果证明了SYK中粒子的非玻色子性质是其物理学的重要组成部分,突出了局部模型和自旋玻璃之间的联系,并提出了关于费米子和/或玻璃性在全息中的作用的重要问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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