内旋转对称性自发破缺的D=2+1（赝）Lorentz不变系统中Goldstone玻色子相互作用
Goldstone Boson Interaction in D=2+1 (Pseudo-)Lorentz-Invariant Systems with a Spontaneously Broken Internal Rotation Symmetry
摘要：
由自发破缺的内部旋转对称性O（$N$）$\to$ O（$N$ -1）表征的系统的低温性质由Goldstone玻色子控制，并且可以在有效拉格朗日场论内系统地导出。在本研究中，我们认为系统生活在两个空间维度，并评估其配分函数在低温下的三个循环顺序。虽然我们的结果对任何这样的系统都是有效的，但在这里我们使用磁性术语，即，我们称之为量子自旋系统。我们讨论了一般$N$中Goldstone玻色子相互作用在压力、交错磁化强度和磁化率中作为外部交错场的函数的符号。事实证明，$d$ =2+1量子XY模型（$N$ =2）和$d$ =2+1海森堡反铁磁体（$N$ =3）是相当特殊的，因为它们代表了压力中的自旋波相互作用在有效展开适用的整个参数范围内是排斥的唯一情况。值得注意的是，$d$ =2+1 XY模型是唯一的系统中的相互作用的贡献，在交错磁化（磁化率）往往是积极的（负）值在低温和弱外场。
英文摘要：
The low-temperature properties of systems characterized by a spontaneously broken internal rotation symmetry, O($N$) $\to$ O($N$-1), are governed by Goldstone bosons and can be derived systematically within effective Lagrangian field theory. In the present study we consider systems living in two spatial dimensions, and evaluate their partition function at low temperatures up to three-loop order. Although our results are valid for any such system, here we use magnetic terminology, i.e., we refer to quantum spin systems. We discuss the sign of the Goldstone boson interaction in the pressure, staggered magnetization, and susceptibility as a function of an external staggered field for general $N$. As it turns out, the $d$=2+1 quantum XY model ($N$=2) and the $d$=2+1 Heisenberg antiferromagnet ($N$=3), are rather special, as they represent the only cases where the spin-wave interaction in the pressure is repulsive in the whole parameter regime where the effective expansion applies. Remarkably, the $d$=2+1 XY model is the only system where the interaction contribution in the staggered magnetization (susceptibility) tends to positive (negative) values at low temperatures and weak external field.
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