Microscopic View of a Two-Dimensional Lattice-Gas Ising System within the Grand Canonical Ensemble

Abstract

A reversible 2D critical transition is observed on the GaAs(001) surface and modeled as a lattice-gas Ising system. Without depositing any material, 2D GaAs islands spontaneously form. The order parameter, four critical exponents, and coupling energies are measured from scanning tunneling microscope images of the microscopic domain structure and correlation functions as a function of temperature and pressure. Unprecedented insight into the domain structure of a 2D Ising system through the critical point and a complete Hamiltonian for modeling the GaAs(001) surface are presented.

Arsenic-rich GaAs(0 0 1) surface structure

“…The only striking difference that these studies did reveal was that the a phase surfaces were more disordered than surfaces prepared in the b-phase. Recent rocking curve RHEED and RDS measurements confirmed that when in the a-phase, surfaces had the same unit cell structure when in the b-phase, namely the b2 model but with slightly different bond lengths [162,156].…”

“…The surface transformation that accompanies the change in RHEED patterns from the flat well-ordered (2 Â 4)-b-phase through the (2 Â 4)-a-phase to the (2 Â 1) phase is a roughening transition [162,31,18,[163][164][165][166]. However, this understanding has only come about very recently due in part to lack of accurate and reproducible temperature control and the driven searches to uncover the atomic structure of the various reconstructions that ignore larger nanoscale structures such as island formation that occur during roughening.…”

Electronic transition from graphite to graphene via controlled movement of the top layer with scanning tunneling microscopy

“…In some instances a phase transition can be identified between the various reconstructions. 3 At the other extreme, a more subtle surface reconstruction can occur which involves only the electron distribution within the material. A prime example is the easily cleaved GaAs(110) surface, which exhibits very weak bonding between layers.…”

Graphene ripples as a realization of a two-dimensional Ising model: A scanning tunneling microscope study

“…Given the coupled two-state nature of graphene ripples and their potential for collective behavior, the celebrated and versatile Ising model might, in principle, be applicable. While Onsager's famous 2D solution was initially applied to the spontaneous magnetization of a 2D square lattice ferromagnet [11,12], through group renormalization [13] it has been established that a wide range of systems belong to the 2D spin-half Ising universality class [14][15][16][17][18][19][20][21]. Bonilla and Carpio treated graphene's individual carbon atoms with the 2D Ising model [22,23] and reproduced the existence of ripples [24,25].…”