论文标题
$ O（N）$模型低于二维的低温行为
Low-temperature behavior of the $O(N)$ models below two dimensions
论文作者
论文摘要
我们研究了$ O（n）$模型的低温阶段的关键行为和性质，该模型处理了$ n $ $ n $的数量和dimension $ d $作为连续变量，重点关注$ d \ leq 2 $和$ n \ leq 2 $ 2 $ Quadrant $（d，n）$平面。我们精确地绘制了$（d，n）$平面的一个区域，其中低温相的特征是代数相关函数衰减，类似于kosterlitz-theless-thouless阶段，但具有与温度无关的异常尺寸$η$。我们重新审查了偶然的汉堡分析，导致了有关$ O（n）$模型的关键指数的非分析行为的预测，并强调了以前在$ d <2 $中对这种方法的不大值所欣赏的后果。特别是，我们讨论了该框架如何导致远程订单的稳定，以$ d <2 $和$ n <2 $的系统中的准远程顺序。随后，在非驾驶重新归一化组的方案中，我们确定了控制准远程有序阶段的低温固定点，并在接近较低的临界维度后证明了临界和低温固定点之间的碰撞。我们评估了关键指数$η（d，n）$和$ν^{ - 1}（d，n）$，并在$ d <2 $中表现出非常好的同意和$ d <2 $的非驾驶重新分析组之间的一个很好的协议。
We investigate the critical behavior and the nature of the low-temperature phase of the $O(N)$ models treating the number of field components $N$ and the dimension $d$ as continuous variables with a focus on the $d\leq 2$ and $N\leq 2$ quadrant of the $(d,N)$ plane. We precisely chart a region of the $(d,N)$ plane where the low-temperature phase is characterized by an algebraic correlation function decay similar to that of the Kosterlitz-Thouless phase but with a temperature-independent anomalous dimension $η$. We revisit the Cardy-Hamber analysis leading to a prediction concerning the nonanalytic behavior of the $O(N)$ models' critical exponents and emphasize the previously not broadly appreciated consequences of this approach in $d<2$. In particular, we discuss how this framework leads to destabilization of the long-range order in favour of the quasi long-range order in systems with $d<2$ and $N<2$. Subsequently, within a scheme of the nonperturbative renormalization group we identify the low-temperature fixed points controlling the quasi long-range ordered phase and demonstrate a collision between the critical and the low-temperature fixed points upon approaching the lower critical dimension. We evaluate the critical exponents $η(d,N)$ and $ν^{-1}(d,N)$ and demonstrate a very good agreement between the predictions of the Cardy-Hamber type analysis and the nonperturbative renormalization group in $d<2$.
