标题： 量子伊辛模型的平均场行为和经典伊辛模型的新绳索展开 显示英文标题

标题： Mean-field behavior of the quantum Ising susceptibility and a new lace expansion for the classical Ising model

摘要： 横场伊辛模型被广泛研究作为最简单的量子自旋系统之一。 已知该模型在临界逆温度$\beta_{\mathrm{c}}$处表现出相变，这由自旋-自旋耦合和横场$q \geq 0$确定。 Björnberg [Commun. Math. Phys., 232 (2013)] 研究了当以适当方式同时改变自旋-自旋耦合$J \geq 0$和$q$时，邻近自旋模型在接近临界点时磁化率的发散速率，温度保持固定。 在本文中，我们固定$J$和$q$并证明当$(\beta_{\mathrm{c}} - \beta)^{-1}$随着$\beta\uparrow\beta_{\mathrm{c}}$变化时，磁化率发散，对于$d>4$假设空间-时间两点函数的红外界限。 关键元素之一是 Björnberg & Grimmett [J. Stat. Phys., 136 (2009)] 和 Crawford & Ioffe [Commun. Math. Phys., 296 (2010)] 中的随机几何表示。 作为副产品，我们推导了经典伊辛模型（即，$q=0$）的新 lace 展开。 显示英文摘要

摘要： The transverse-field Ising model is widely studied as one of the simplest quantum spin systems. It is known that this model exhibits a phase transition at the critical inverse temperature $\beta_{\mathrm{c}}$, which is determined by the spin-spin couplings and the transverse field $q \geq 0$. Bj\"ornberg [Commun. Math. Phys., 232 (2013)] investigated the divergence rate of the susceptibility for the nearest-neighbor model as the critical point is approached by simultaneously changing the spin-spin coupling $J \geq 0$ and $q$ in a proper manner, with fixed temperature. In this paper, we fix $J$ and $q$ and show that the susceptibility diverges as $(\beta_{\mathrm{c}} - \beta)^{-1}$ as $\beta\uparrow\beta_{\mathrm{c}}$ for $d>4$ assuming an infrared bound on the space-time two-point function. One of the key elements is a stochastic-geometric representation in Bj\"ornberg & Grimmett [J. Stat. Phys., 136 (2009)] and Crawford & Ioffe [Commun. Math. Phys., 296 (2010)]. As a byproduct, we derive a new lace expansion for the classical Ising model (i.e., $q=0$).