论文标题
NAMBU-GOLDSTONE横向相关性的幂律衰减指数
Power-Law Decay Exponents of Nambu-Goldstone Transverse Correlations
论文作者
论文摘要
我们在三个或更高尺寸的高素质晶格上研究了量子抗铁磁的海森堡模型$ d \ ge 3 $。当相变发生在连续的对称性破裂时，通过应用无限弱的弱对称性断裂场获得的非消失的自发磁化等于在零或非零低温下的最大自发磁化。另外，无限 - 体积极限中的横向相关性表现出nambu-goldstone型缓慢衰变。在本文中，我们假设横向相关性与距离的横向相关性衰减。在此假设下，我们证明，在非零低温下的功率等于$ 2-D $，而在零温度下等于$ 1-D $。该方法还应用于三个或更高维度的非零低温下的量子XY模型和经典的Heisenberg模型。在非零低温下，由相同的$ 2-D $给出了产生的功率。
We study a quantum antiferromagnetic Heisenberg model on a hypercubic lattice in three or higher dimensions $d\ge 3$. When a phase transition occurs with the continuous symmetry breaking, the nonvanishing spontaneous magnetization which is obtained by applying the infinitesimally weak symmetry breaking field is equal to the maximum spontaneous magnetization at zero or non-zero low temperatures. In addition, the transverse correlation in the infinite-volume limit exhibits a Nambu-Goldstone-type slow decay. In this paper, we assume that the transverse correlation decays by power law with distance. Under this assumption, we prove that the power is equal to $2-d$ at non-zero low temperatures, while it is equal to $1-d$ at zero temperature. The method is applied also to a quantum XY model and a classical Heisenberg model at non-zero low temperatures in three or higher dimensions. The resulting power is given by the same $2-d$ at non-zero low temperatures.
