The 2D spin-1 ANNNI model is studied using an iterative method, the method of ring recurrence. The phase diagram is obtained numerically using matrices of order 9. The authors find the phase diagram to be generally similar to that of the 2D spin-1/2 ANNNI model.
The authors study in detail the short-range order at low temperature in a one-dimensional Ising model with competing interactions by studying various staggered susceptibilities. From this they get a 'phase diagram' which divides regions of various dominant short-range orders. This phase diagram is shown to resemble qualitatively the low-temperature phase diagram of the anisotropic next-nearest-neighbour interaction Ising (ANNNI) model in higher dimensions. They argue that this method of studying a corresponding one-dimensional problem may be useful to understand the phase structure of complex higher-dimensional systems.
We investigate the phase diagram of a generalized spin-1/2 quantum antiferromagnet on a ladder with rung, leg, diagonal, and ring-exchange interactions. We consider the exactly soluble models associated with the problem, obtain the exact ground states which exist for certain parameter regimes, and apply a variety of perturbative techniques in the regime of strong ring-exchange coupling. By combining these approaches with considerations related to the discrete Z4 symmetry of the model, we present the complete phase diagram.
A central question on Kitaev materials is the effects of additional couplings on the Kitaev model, which is proposed to be a candidate for realizing topological quantum computations.However, two spatial dimensions typically suffer the difficulty of lacking controllable approaches.In this work, using a combination of powerful analytical and numerical methods available in one dimension, we perform a comprehensive study on the phase diagram of a one-dimensional version of the spin-1/2 Kitaev-Heisenberg-Gamma model in its full parameter space.A strikingly rich phase diagram is found with nine distinct phases, including four Luttinger liquid phases, a ferromagnetic phase, a Néel ordered phase, an ordered phase of distorted-spiral spin alignments, and two ordered phases, which both break a D 3 symmetry albeit in different ways, where D 3 is the dihedral group of order six.Our work paves the way for studying one-dimensional Kitaev materials and may provide hints to the physics in higher-dimensional situations.
Two-dimensional spin 1/2 antiferromagnetic Heisenberg models are numerically studied using Entanglement Perturbation Theory, where the ground state wave function is described by a product of local matrices defined at every site, and each matrix is optimized variationally to minimize the energy. We first apply this method for the spin 1/2 antiferromagnetic Heisenberg model on the square lattices to reproduce correctly the known ground state energy and the spin structure factors. Then, we study the spin 1/2 antiferromagnetic Heisenberg model on the triangular lattice with spatially anisotropic nearest neighbor couplings, J and J ', to establish the ground state phase diagram as a function of J'/ J.
The phase diagrams of general q-state planar spin models on a square lattice are studied for $q=4\ensuremath{-}7$. The phase diagrams are calculated by a variational method and the infinitesimal Migdal renormalization-group (RG) transformations. Since the Migdal RG commutes with the self-dual transformations of Z(q) models, one expects reliable phase diagrams (but not accurate critical exponents). In fact all exactly known critical points are reproduced by our calculations together with a fair numerical simulation of lines of critical points. Our results clearly indicate the existence of massless phases for q=6and7 but are inconclusive for q=5. More accurate methods are needed to determine the phase structure of the Z(5) model; see, for example, the finite-lattice approximation of Roomany and Wyld (preceding paper).