论文标题
非整合ISING模型的能量相关性：气缸中的缩放限制
Energy correlations of non-integrable Ising models: The scaling limit in the cylinder
论文作者
论文摘要
我们考虑了一类不可积分的2D ISING模型，除了最近的邻居耦合外，哈密顿量即使在自旋翻转下，也包括弱的多旋转相互作用。我们研究了任意纵横比的圆柱域中的模型，并证明，在缩放极限中，多点能量相关性收敛到与圆柱体中最近邻居ising模型的相同限制相关性，并具有重新分配的耦合，直至整体多重式常数，独立于近距离的形状和大小。该证明是基于相关性生成函数的表示，其相关性是非高斯格拉斯曼积分和其建设性的重质化组（RG）分析。 与以前的作品相比，关键的技术新颖性是对边界校正对RG流动的影响的系统分析，特别是证明边界运营商的缩放维度比其大量对应物更好。基于费米子绿色功能的基于近似图像规则的取消机制对于控制边界项的RG流动至关重要。
We consider a class of non-integrable 2D Ising models, whose Hamiltonian, in addition to the nearest neighbor couplings, includes weak multi-spin interactions, even under spin flip. We study the model in cylindrical domains of arbitrary aspect ratio and prove that, in the scaling limit, the multipoint energy correlations converge to the same limiting correlations as those of the nearest-neighbor Ising model in the cylinder with renormalized couplings, up to an overall multiplicative constant, independent of the shape and size of the domain. The proof is based on a representation of the generating function of correlations in terms of a non-Gaussian Grassmann integral, and a constructive Renormalization Group (RG) analysis thereof. A key technical novelty compared with previous works is a systematic analysis of the effect of the boundary corrections to the RG flow, in particular a proof that the scaling dimension of boundary operators is better by one dimension than their bulk counterparts. A cancellation mechanism based on an approximate image rule for the fermionic Green's function is of crucial importance for controlling the RG flow of the marginal boundary terms.
