Incommensurate structures studied by a modified Density Matrix Renormalization Group Method

TL;DR

This paper introduces a modified DMRG method to study incommensurate phases in classical 2D models, revealing the separation of disordered and commensurate phases and confirming the absence of Lifshitz points.

Contribution

A novel modification of the DMRG method applied to classical 2D models, providing new insights into their phase diagrams and incommensurate phases.

Findings

Incommensurate phase separates disordered and commensurate phases.

Confirmed the non-existence of Lifshitz points in both models.

Phase diagrams exhibit complex structures with incommensurate phases.

Abstract

A modified density matrix renormalization group (DMRG) method is introduced and applied to classical two-dimensional models: the anisotropic triangular nearest- neighbor Ising (ATNNI) model and the anisotropic triangular next-nearest-neighbor Ising (ANNNI) model. Phase diagrams of both models have complex structures and exhibit incommensurate phases. It was found that the incommensurate phase completely separates the disordered phase from one of the commensurate phases, i. e. the non-existence of the Lifshitz point in phase diagrams of both models was confirmed.