标题： 关于霍恩伯格-默里温格定理及其局限性 显示英文标题

标题： On the Hohenberg-Mermin-Wagner theorem and its limitations

摘要： 大约五十年前，皮埃尔·霍伯格提出了一个严格的证明，证明在有限温度下二维超流体或超导体中不存在长程序。该证明立即被N. D. 梅尔明和H. 韦格纳扩展到海森堡铁磁体和反铁磁体，不久之后，梅尔明又证明了在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。在本文中，我们对霍伯格-梅尔明-韦格纳定理进行了扩展，以提供一个严格的证明，证明在没有自旋轨道耦合或磁偶极相互作用的巡游电子系统中，不可能存在长程铁磁序。我们还评论了一些情况，这些情况下有强有力的论据表明长程序是不可能的，但还没有给出严格的证明，以及一些情况，例如具有长程相互作用的磁体，或者二维晶体中的取向序，其中长程序可能发生并破坏连续对称性。 显示英文摘要

摘要： Just over fifty years ago, Pierre Hohenberg developed a rigorous proof of the non-existence of long-range order in a two-dimensional superfluid or superconductor at finite temperatures. The proof was immediately extended by N. D. Mermin and H. Wagner to the Heisenberg ferromagnet and antiferromagnet, and shortly thereafter, by Mermin to prove the absence of translational long-range order in a two-dimensional crystal, whether in quantum or classical mechanics. In this paper, we present an extension of the Hohenberg-Mermin-Wagner theorem to give a rigorous proof of the impossibility of long-range ferromagnetic order in an itinerant electron system without spin-orbit coupling or magnetic dipole interactions. We also comment on some situations where there are compelling arguments that long-range order is impossible but no rigorous proof has been given, as well as situations, such as a magnet with long range interactions, or orientational order in a two-dimensional crystal, where long-range order can occur that breaks a continuous symmetry.