Bifurcation analysis and phase diagram of a spin-string model with buckled states
arXiv:1708.07990 · doi:10.1103/PhysRevE.96.062147
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.
15 pages, 7 figures
References in corpus (13)
- The structure of suspended graphene sheets
- Electron-induced rippling in graphene
- Anomalous Dynamical Behavior of Freestanding Graphene Membranes
- Driving-induced crossover: from classical criticality to self-organized criticality
- Training-induced criticality in martensites
- Graphene Ripples as a Realization of a Two-Dimensional Ising Model: A Scanning Tunneling Microscope Study
- Theory of the spontaneous buckling of doped graphene
- Model of ripples in graphene
- Ripples in a graphene membrane coupled to Glauber spins
- STM driven transition from rippled to buckled graphene in a spin-membrane model
- Rippling transition from electron-induced condensation of curvature field in graphene
- Phase transitions in a mechanical system coupled to Glauber spins
- Spin-oscillator model for DNA/RNA unzipping by mechanical force