Genzor JGendiar AYING-JER KAO2022-04-252022-04-25202224700045https://www.scopus.com/inward/record.uri?eid=2-s2.0-85125598350&doi=10.1103%2fPhysRevE.105.024124&partnerID=40&md5=a0ad8f7beaba509212815c934bdd83fehttps://scholars.lib.ntu.edu.tw/handle/123456789/606833We generalize a tensor-network algorithm to study the thermodynamic properties of self-similar spin lattices constructed on a square-lattice frame with two types of couplings, J1 and J2, chosen to transform a regular square lattice (J1=J2) onto a fractal lattice if decreasing J2 to zero (the fractal fully reconstructs when J2=0). We modified the higher-order tensor renormalization group (HOTRG) algorithm for this purpose. Single-site measurements are performed by means of so-called impurity tensors. So far, only a single local tensor and uniform extension-contraction relations have been considered in HOTRG. We introduce 10 independent local tensors, each being extended and contracted by 15 different recursion relations. We applied the Ising model to the J1-J2 planar fractal whose Hausdorff dimension at J2=0 is d(H)=ln12/ln4?1.792. The generalized tensor-network algorithm is applicable to a wide range of fractal patterns and is suitable for models without translational invariance. ? 2022 American Physical Society.Crystal lattices; Fractal dimension; Ising model; Statistical mechanics; Thermodynamic properties; Fractal lattices; Higher-order tensor; Network algorithms; Network methods; Renormalization group; Self-similar; Single sites; Spin lattices; Square lattices; Tensor renormalization; Tensorsjournal article10.1103/PhysRevE.105.0241242-s2.0-85125598350