Physical limitations of the Hohenberg-Mermin-Wagner theorem
Grgur Palle, D. K. Sunko
备注：
This version (v2) is the authors' version which was accepted for publication. The previous version (v1), which was never submitted itself, contains additional material which some readers may find interesting
The Hohenberg-Mermin-Wagner (HMW) theorem states that infrared (IR) fluctuations prevent long-range order which breaks continuous symmetries in two dimensions (2D), at finite temperatures. We note that the theorem becomes physically effective for superconductivity (SC) only for astronomical sample sizes, so it does not prevent 2D SC in practice. We systematically explore the sensitivity of the magnetic and SC versions of the theorem to finite-size and disorder effects. For magnetism, finite-size effects, disorder, and perpendicular coupling can all restore the order parameter at a non-negligible value of $T_c$ equally well, making the physical reason for finite $T_c$ sample-dependent. For SC, an alternative version of the HMW theorem is presented, in which the temperature cutoff is set by Cooper pairing, in place of the Fermi energy in the standard version. It still allows 2D SC at $2$--$3$ times the room temperature when the interaction scale is large and Cooper pairs are small, the case with high-$T_c$ SC in the cuprates. Thus IR fluctuations do not prevent 2D SC at room temperatures in samples of any reasonable size, by any known version of the HMW argument. A possible approach to derive mechanism-dependent upper bounds for SC $T_c$ is pointed out.
The inverse Mermin-Wagner theorem for classical spin models on graphs
在这封信中，我们提出的Mermin-Wagner定理在图上的反转，通过证明在有限温度下的自发磁化的存在性的经典自旋模型的瞬态平均（TOA）图，即图中的随机步行者返回到其起点的平均概率$\bar F < 1$。这个结果，这是证明了模型的O（n）对称性，包括作为一个特殊的情况$n=1$，提供了一个非常普遍的条件，自发对称性破缺的非均匀结构，即使是伊辛模型。
On the Hohenberg-Mermin-Wagner theorem and its limitations
就在50多年前，皮埃尔·霍恩伯格（Pierre Hohenberg）对有限温度下二维超流体或超导体中不存在长程序进行了严格的证明。这个证明立即被N. D. Mermin和H.瓦格纳到海森堡铁磁体和反铁磁体，此后不久，梅尔明证明了二维晶体中不存在平移长程序，无论是在量子力学还是经典力学中。本文推广了Hohenberg-Mermin-Wagner定理，严格证明了在没有自旋轨道耦合和磁偶极相互作用的巡游电子系统中不可能存在长程铁磁有序.我们还评论了一些情况下，有令人信服的论点，长程序是不可能的，但没有严格的证明已经给出，以及情况下，如一个磁铁与长程相互作用，或在一个二维晶体的取向顺序，其中长程序可以发生，打破了连续的对称性。
Two-Dimensional Phase Transitions in Classical Systems: 60 Years after the Hohenberg-Mermin-Wagner Theorem
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；State Key Laboratory of Surface Physics and Department of Physics, Fudan University（复旦大学表面物理国家重点实验室和物理系）
