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.
Integrable, Mixed, and Chaotic Dynamics in a Single All-to-All Ising Spin Model
Research Centre for Quantum Information, Institute of Physics, Slovak Academy of Sciences（斯洛伐克科学院物理研究所量子信息研究中心）；Institute for Quantum Science and Technology, University of Calgary（卡尔加里大学量子科学与技术研究所）；Department of Physics, Lakehead University（拉筹伯大学物理系）；Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien（维也纳科技大学原子研究所维也纳量子科学与技术中心）
