Bifurcation analysis and phase diagram of a spin-string model with buckled states

TL;DR

This paper investigates a one-dimensional spin-string model with competing interactions, revealing a complex phase diagram of rippled and buckled states, and uses bifurcation theory to analyze phase stability and underlying physical mechanisms.

Contribution

It provides a detailed bifurcation analysis of the one-dimensional model's phase diagram, enhancing understanding of phase stability and transitions in spin-string systems.

Findings

Complex phase diagram with flat, rippled, and buckled states

First and second order transition lines identified

Bifurcation theory elucidates phase stability mechanisms

Abstract

We analyze a one-dimensional spin-string model, in which string oscillators are linearly coupled to their two nearest neighbors and to Ising spins representing internal degrees of freedom. String-spin coupling induces a long-range ferromagnetic interaction among spins that competes with a spin-spin antiferromagnetic coupling. As a consequence, the complex phase diagram of the system exhibits different flat rippled and buckled states, with first or second order transition lines between states. The two-dimensional version of the model has a similar phase diagram, which has been recently used to explain the rippled to buckled transition observed in scanning tunnelling microscopy experiments with suspended graphene sheets. Here we describe in detail the phase diagram of the simpler one-dimensional model and phase stability using bifurcation theory. This gives additional insight into the physical mechanisms underlying the different phases and the behavior observed in experiments.