Ripples in a graphene membrane coupled to Glauber spins

Abstract

We propose a theory of ripples in suspended graphene sheets based on two-dimensional elasticity equations that are made discrete on the honeycomb lattice and then periodized. At each point carbon atoms are coupled to Ising spins whose values indicate the atoms local trend to move vertically off-plane. The Ising spins are in contact with a thermal bath and evolve according to Glauber dynamics. In the limit of slow spin flip compared to membrane vibrations, ripples with no preferred orientation appear as long-lived metastable states for any temperature. Numerical solutions confirm this picture.

15 pages, 4 figures. arXiv admin note: text overlap with arXiv:1211.0527

References in corpus (14)

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• Phase transitions in a mechanical system coupled to Glauber spins

Cited by in corpus (5)

• Graphene Ripples as a Realization of a Two-Dimensional Ising Model: A Scanning Tunneling Microscope Study
• Model of ripples in graphene
• Bifurcation analysis and phase diagram of a spin-string model with buckled states
• STM driven transition from rippled to buckled graphene in a spin-membrane model
• Large-scale critical behavior of the rippling phase transition for graphene membranes