Physical realization of two-dimensional Ising critical phenomena: Oxygen chemisorbed on the W(112) surface

Dimer Coupling Energies of the Si(001) Surface

The coupling energies between the buckled dimers of the Si(001) surface were determined through analysis of the anisotropic critical behavior of its order-disorder phase transition. Spot profiles in high-resolution low-energy electron diffraction as a function of temperature were analyzed within the framework of the anisotropic two-dimensional Ising model. The validity of this approach is justified by the large ratio of correlation lengths, ξ_{∥}^{+}/ξ_{⊥}^{+}=5.2 of the fluctuating c(4×2) domains above the critical temperature T_{c}=(190.6±10)  K. We obtain effective couplings J_{∥}=(-24.9±1.3)  meV along the dimer rows and J_{⊥}=(-0.8±0.1)  meV across the dimer rows, i.e., antiferromagneticlike coupling of the dimers with c(4×2) symmetry.

Universal window for two-dimensional critical exponents

Two-dimensional condensed matter is realized in increasingly diverse forms that are accessible to experiment and of potential technological value. The properties of these systems are influenced by many length scales and reflect both generic physics and chemical detail. To unify their physical description is therefore a complex and important challenge. Here we investigate the distribution of experimentally estimated critical exponents, β, that characterize the evolution of the order parameter through the ordering transition. The distribution is found to be bimodal and bounded within a window ∼0.1≤β≤0.25, facts that are only in partial agreement with the established theory of critical phenomena. In particular, the bounded nature of the distribution is impossible to reconcile with the existing theory for one of the major universality classes of two-dimensional behaviour-the XY model with four-fold crystal field-which predicts a spectrum of non-universal exponents bounded only from below. Through a combination of numerical and renormalization group arguments we resolve the contradiction between theory and experiment and demonstrate how the 'universal window' for critical exponents observed in experiment arises from a competition between marginal operators.

Intrinsic character of the (3 x 3) to (square root 3 x square root 3) phase transition in Pb/Si(111)

We have investigated the (3 x 3) to (square root 3 x square root 3) reversible phase transition in Pb/Si(111) by means of variable temperature scanning tunneling microscopy and density functional first-principles calculations. By tracking exactly the same regions of the surface with atomic resolution in a temperature range between 40 and 200 K, we have observed the phase transition in real time. The ability to prepare and track exceptionally large domains without defects has allowed us to detect the intrinsic character of the phase transition at temperatures around 86 K. This intrinsic character is in full agreement with our first-principles calculations. Moreover, our results show that the hypothesis that point defects play a fundamental role as the driving force, reported for similar systems, can be discarded for Pb/Si(111).

Microscopic view of a two-dimensional lattice-Gas ising system within the grand canonical ensemble

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.