Renormalization group studies of phase diagrams of Ising and XY-model films of variable thickness

Néstor Parga, Johannes E. Van Himbergen

Abhishek Samlodia, Vamika Longia, Raghav G. Jha +1 more

We use the higher-order tensor renormalization group method to study the two-dimensional generalized XY model that admits integer and half-integer vortices. This model is the deformation of the classical XY model and has a rich phase structure consisting of nematic, ferromagnetic, and disordered phases and three transition lines belonging to the Berezinskii-Kosterlitz-Thouless and Ising class. We explore the model for a wide range of temperatures, T , and the deformation parameter, Δ , and compute specific heat along with integer and half-integer magnetic susceptibility, finding both Berezinskii-Kosterlitz-Thouless-like and Ising-like transitions and the region where they meet. Published by the American Physical Society 2024

A. Benyoussef, Hamid Ez-zahraouy A

Aykut Erbaş, Aslı Tuncer, Burcu Yücesoy +1 more

Hierarchical lattices that constitute spatially anisotropic systems are introduced. These lattices provide exact solutions for hierarchical models and, simultaneously, approximate solutions for uniaxially or fully anisotropic d = 3 physical models. The global phase diagrams, with d = 2 and d = 1 to d = 3 crossovers, are obtained for Ising and XY magnetic models and percolation systems, including crossovers from algebraic order to true long-range order.

Xuan-Zhang Wang, Yan Zhao

Takahiro Murashima, Keigo Hijii, K. Nomura +1 more

The one dimensional S=1 XXZ model with next-nearest-neighbor interaction $α$ and Ising-type anisotropy $Δ$ is studied by using a numerical diagonalization technique. We discuss the ground state phase diagram of this model numerically by the twisted-boundary-condition level spectroscopy method and the phenomenological renormalization group method, and analytically by the spin wave theory. We determine the phase boundaries among the XY phase, the Haldane phase, the ferromagnetic phase and the Néel phase, and then we confirm the universality class. Moreover, we map this model onto the non-linear $σ$ model and analyze the phase diagram in the $α$ $\ll$ -1 and $Δ$ $\sim$ 1 region by using the renormalization group method.