Physics
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Item Triangular lattice gas with first- and second-neighbor exclusions: Continuous transition in the four-state Potts universality class(American Physical Society, 1984) Bartelt, N. C.; Einstein, Theodore L.Using phenomenological renormalization (transfer-matrix scaling), we have reexamined the phase transition of a triangular lattice gas with particles having both nearest- and second-nearest-neighbor exclusions. Widely accepted classical studies indicated that disordering of the ordered (p(2x2)) state is first order. In contradiction, we show that the transition is second order; its exponents are consistent with the four-state Potts model universality class, in accord with its Landau-Ginzburg-Wilson Hamiltonian classification.Item Summary Abstract: Relationship between many-parameter lattice gas systems and simpler models: Easy approximations for Tc(AIP, 1984) Bartelt, N. C.; Einstein, Theodore L.; Williams, Ellen D.Item Proposed decorated lattice-gas model of H/Pd(100)(American Physical Society, 1987) Bartelt, N. C.; Einstein, Theodore L.A Comment on the Letter by D. Tomanek, S. G. Louie, and C.-T. Chan, Phys. Rev. Lett. 57, 2594 (1986); 58, 287(E) (1987).Item Phase diagram and critical properties of a two-dimensional lattice-gas model of oxygen ordering in YBa2Cu3Oz(American Physical Society, 1989) Bartelt, N. C.; Einstein, Theodore L.; Wille, L. T.Using transfer-matrix finite-size scaling, we investigate a square lattice-gas model for the oxygen ordering in YBa2Cu3Oz, which reproduces the experimentally observed orthorhombic and double-cell ordered phases. Contrary to the results of cluster-variational methods of calculation, the phase boundary between the (disordered) tetragonal and double-cell phases is continuous, as is the boundary between the orthorhombic and double-cell phases. Critical properties of the model can be understood by drawing an analogy with the Ashkin-Teller model; numerical results are consistent with this picture. At low temperature and low oxygen concentration, there is complicated behavior, possibly indicative of a second orthorhombic phase.Item Structure factors associated with the continuous melting of two-dimensional lattice gases(American Physical Society, 1987) Bartelt, N. C.; Einstein, Theodore L.; Roelofs, L. D.We study the temperature dependence of the structure factors of two lattice gases which undergo order-disorder phase transitions. Our goal is to determine how much information about the critical behavior of these phase transitions a low-energy electron-diffraction experiment might obtain. We use Monte Carlo simulation to compute the structure factors.Item Transfer-matrix approach to estimating coverage discontinuities and multicritical-point positions in two-dimensional lattice-gas phase diagrams(American Physical Society, 1986) Bartelt, N. C.; Einstein, Theodore L.; Roelofs, L. D.We present a method of computing coverage discontinuities in two-dimensional lattice-gas phase diagrams using transfer matrices. By applying the method to Baxter’s generalized hard-square model, we find good agreement with exact results. This method also can be used to estimate the position of multicritical points, and we again find good agreement with exact results and with previous work on the Ising metamagnet. We discuss the transfer-matrix eigenvalue spectrum around an Ising tricritical point and verify the prediction of conformal invariance that the finite-size scaling behavior of each of the leading eigenvalues is governed by a different critical exponent at the critical point. We show numerically that the finite-size convergence of the free energy at the (Ising-like) tricritical point of Baxter’s model is consistent with a conformal anomaly of (7/10). We show that the justification of a commonly used method to locate multicritical points using simultaneous scaling of the correlation length and the "persistence length" is misleading. Finally we suggest a method of estimating the position of multicritical points using information from only one strip width.Item Structure factors associated with the melting of a (31) ordered phase on a centered-rectangular lattice gas: Effective scaling in a three-state chiral-clock-like model(American Physical Society, 1987) Bartelt, N. C.; Einstein, Theodore L.; Roelofs, L. D.By computing the structure factor through the melting transition of a commensurate (3x1) phase in a version of Baxter’s generalized hard hexagon model, we simulate what might be observed in diffraction experiments (especially those using low-energy electrons) on chemisorption systems which have similar Landau-Ginzburg-Wilson Hamiltonians. In the commensurate and disordered phases we observe that the shift of the peak of the critical scattering from the commensurate position is roughly proportional to the inverse correlation length in the reduced temperature range 0.015–0.15. The proportionality constant appears to depend on the position of the transition on the phase boundary (i.e., on the chemical potential). We see no sign of an incommensurate floating phase between the disordered and commensurate phases. Effective critical exponents are consistent with those expected from the three-state Potts model. To the precision of this calculation (a few percent), the structure factor scales over approximately 10% of the Brillouin-zone area.Item Structure factors associated with melting of a p(22) ordered phase on a honeycomb lattice gas: Possible critical scattering at a first-order transition(American Physical Society, 1987) Bartelt, N. C.; Einstein, Theodore L.; Roelofs, L. D.We study the order-disorder transition of a p(2x2) ordered state on a honeycomb lattice using Monte Carlo calculations of the structure factor. We observe a correlation length which gets large as the transition is approached; the effective critical exponents are close to the exponents characterizing a discontinuity fixed point and similar to those we observe for the first-order transition of the eight-state Potts model. We also discuss how observation of the outer integral-order diffraction beams gives information about the relevance of the field which distinguishes the two triangular sublattices of the honeycomb lattice.Item Summary Abstract: Structure factors of two?dimensional lattice gases: Theoretical investigation of some aspects of the capability of low?energy electron diffraction to measure critical phenomena of surface phase transitions(AIP, 1987) Einstein, Theodore L.; Bartelt, N. C.; Roelofs, L. D.Item Two-dimensional ordering of chlorine on Ag(100)(American Physical Society, 1985) Taylor, David E.; Williams, Ellen D.; Park, Robert L.; Bartelt, N. C.; Einstein, Theodore L.Chlorine adsorption on Ag(100) saturates at (1/2) monolayer (ML) in a c(2x2) structure. Desorption occurs above 650 K without disordering. The sticking coefficient remains constant to within 0.05 ML of saturation, consistent with the existence of a highly mobile precursor to adsorption. The c(2x2) structure forms at a critical coverage of 0.394+-0.007 ML at room temperature. This is slightly higher than the critical coverage of the hard-square model (0.368 ML), suggesting the influence of further-neighbor interactions.