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

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.

arXiv comment15 pages, 7 figures

References in corpus (19)

• The structure of suspended graphene sheets
• Intrinsic ripples in graphene
• 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
• Collective excitations in a large-d model for graphene
• Theory of the spontaneous buckling of doped graphene
• Model of ripples in graphene
• Critical radius and temperature for buckling in graphene
• Ripples in a string coupled to Glauber spins
• Ripples in a graphene membrane coupled to Glauber spins
• Ripples in hexagonal lattices of atoms coupled to Glauber spins
• STM driven transition from rippled to buckled graphene in a spin-membrane model
• Nonequilibrium dynamics of a fast oscillator coupled to Glauber spins
• 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

Cited by in corpus (9)

• Statistical Mechanics of Systems with Negative Temperature
• Buckling of thermalized elastic sheets
• Thermal control of nucleation and propagation transition stresses in discrete lattices with non-local interactions and non-convex energy
• Bending rigidity, sound propagation and ripples in flat graphene
• Tuning and jamming reduced to their minima
• Derivation of a Langevin equation in a system with multiple scales: the case of negative temperatures
• A numerical study of the rippling instability driven by electron-phonon coupling in graphene
• Large-scale critical behavior of the rippling phase transition for graphene membranes
• Buckling in a rotationally invariant spin-elastic model