Topological floating phase in a spatially anisotropic frustrated Ising model

TL;DR

This study investigates a two-dimensional anisotropic frustrated Ising model, revealing an intermediate topological floating phase and a transition to a stripe-ordered phase through extensive simulations and analytical methods.

Contribution

It provides the first detailed evidence for a topological floating phase in an anisotropic frustrated Ising model using combined Monte Carlo simulations and Villain-Bak theory.

Findings

Identification of an incommensurate algebraically-ordered floating phase

Observation of a transition to a stripe-ordered antiferromagnetic phase

Quantitative phase diagram including the floating phase

Abstract

We present new results for the ordering process of a two-dimensional Ising model with anisotropic frustrating next-nearest-neighbor interactions. We concentrate on a specific wide temperature and parameter region to confirm the existence of two particular phases of the model. The first phase is an incommensurate algebraically-ordered (floating) phase emerging at the transition from the paramagnetic high-temperature phase. Then the model undergoes a transition to an antiferromagnetically ordered second phase with diagonal ferromagnetic stripes (ordering wave vector $\vec q = (\pi/2, \pi/2)$). We analyze the unconventional features appearing in several observables, e.g., energy, structure factors, and correlation functions by means of extensive Monte-Carlo simulations and examine carefully the influence of the lattice sizes. For the analytical study of the intermediate phase the Villain-Bak theory is adapted for the present model. Combining both the numerical and analytical work we present the quantitative phase diagram of the model, and, in particular, argue in favor of an intermediate topological floating phase.