Ripples in hexagonal lattices of atoms coupled to Glauber spins

Abstract

A system of atoms connected by harmonic springs to their nearest neighbors on a lattice is coupled to Ising spins that are in contact with a thermal bath and evolve under Glauber dynamics. Assuming a nearest-neighbor antiferromagnetic interaction between spins, we calculate analytically the equilibrium state. On a one-dimensional attice, the system exhibits first and second order phase transitions. The order parameters are the total magnetization and the number of spin pairs in an antiferromagnetic configuration. On a hexagonal two dimensional lattice, spins interact with their nearest-neighbors and next-nearest-neighbors. Together with the coupling to atoms, these interactions produce a complex behavior that is displayed on a phase diagram. There are: ordered phases associated to ripples with atomic wavelength and antiferromagnetic order, ordered phases associated to ripples with nanometer wavelengths and ferromagnetic order, disordered glassy phases, and other phases presenting stripes formed by different domains. These static phases are discussed in relation to existing experiments and results for other models found in the literature.

accepted for publication in JSTAT

References in corpus (17)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Two Dimensional Atomic Crystals
• The structure of suspended graphene sheets
• Electron scattering on microscopic corrugations in graphene
• Graphene as an electronic membrane
• Gauge field induced by ripples in graphene
• Electron-induced rippling in graphene
• Roughness of undoped graphene and its short-range induced gauge field
• Periodized discrete elasticity models for defects in graphene
• Thermodynamics of quantum crystalline membranes
• 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
• Model of ripples in graphene
• Ripples in a graphene membrane 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

Cited by in corpus (11)

• Fluctuation-induced current from freestanding graphene: toward nanoscale energy harvesting
• Buckling of thermalized elastic sheets
• Critical radius and temperature for buckling in graphene
• Buckling and metastability in membranes with dilation arrays
• 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
• Bending rigidity, sound propagation and ripples in flat graphene
• 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