论文标题
二维RP $^{N-1} $模型的渐近低温行为
Asymptotic low-temperature behavior of two-dimensional RP$^{N-1}$ models
论文作者
论文摘要
我们研究了二维（2D）RP $^{n-1} $模型的低温行为，其特征是全局O（$ n $）对称性和局部$ {\ Mathbb Z} _2 $对称性。对于$ n = 3 $，我们对四个不同的2D晶格模型进行大规模模拟：两个标准晶格模型和两个不同的约束模型。我们还考虑了参数值的约束混合O（3）-RP $^2 $模型，使矢量相关始终是无序的。我们发现所有这些模型都显示出相同的有限尺寸缩放（FSS）行为，因此属于同一普遍性类别。但是，这些FSS曲线与2D O（3）$σ$模型中计算的曲线不同，这表明存在独特的2D RP $^2 $通用类。我们还为$ n = 4 $进行了模拟，相应的FSS结果也支持RP $^3 $通用类的存在，与O（4）One不同。
We investigate the low-temperature behavior of two-dimensional (2D) RP$^{N-1}$ models, characterized by a global O($N$) symmetry and a local ${\mathbb Z}_2$ symmetry. For $N=3$ we perform large-scale simulations of four different 2D lattice models: two standard lattice models and two different constrained models. We also consider a constrained mixed O(3)-RP$^2$ model for values of the parameters such that vector correlations are always disordered. We find that all these models show the same finite-size scaling (FSS) behavior, and therefore belong to the same universality class. However, these FSS curves differ from those computed in the 2D O(3) $σ$ model, suggesting the existence of a distinct 2D RP$^2$ universality class. We also performed simulations for $N=4$, and the corresponding FSS results also support the existence of an RP$^3$ universality class, different from the O(4) one.
