Phase diagrams for a square lattice with two- and three-body interactions
TL;DR: In this paper, the phase diagram for a model with the Ising Hamiltonian extended to accomodate couplings beyond the simplest nearest neighbor has been studied for hydrogen on Pd(100) and shown qualitative agreement with experiment at high temperatures but with a too narrow ordered region.
About: This article is published in Surface Science.The article was published on 1982-07-02. It has received 10 citations till now. The article focuses on the topics: Ising model & Renormalization group.
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TL;DR: In this article, it is shown that the (three-dimensional) tetragonal to orthorhombic transition in the 1-2-3 superconducting compound can be mapped onto a two-dimensional Ising model with anisotropic second neighbor effective pair interactions.
Abstract: It is shown that the (three-dimensional) tetragonal to orthorhombic transition in the 1-2-3 superconducting compound can be mapped onto a two-dimensional Ising model with anisotropic second neighbor effective pair interactions The Cluster Variation Method (CVM) has been used to calculate a phase diagram based on interaction parameters provided by first principles linear muffin-tin orbital-atomic sphere approximation (LMTO-ASA) calculations performed by P Sterne at Lawrence Livermore National Laboratory At high temperature, agreement with experimental phase transition data is excellent At low temperatures, two-dimensional ordering gives way to quasi one-dimensional states of order as described by the linear chain Ising model for which the thermodynamics are known exactly Structures produced by Monte Carlo simulation and theoretical diffraction patterns are in striking agreement with recent experimental results
140 citations
TL;DR: In this article, the ordering in the Cu O basal plane of YBa2Cu3Oz is investigated as a function of oxygen content and temperature, and several phase diagrams are calculated by means of the Cluster Variation Method applied to asymmetric two-dimensional Ising models.
Abstract: The ordering in the Cu O basal plane of YBa2Cu3Oz is investigated as a function of oxygen content and temperature. Several phase diagrams are calculated by means of the Cluster Variation Method applied to asymmetric two-dimensional Ising models. The interaction parameters selected guarantee the stability of the orthorhombic structures near z=7, and, for certain choices, also include a double-cell phase around z=6.5. O Cu O correlations are investigated as a function of temperature and concentrations. Calculated orthorhombic to tetragonal transition temperatures and concentrations for various oxygen partial pressures are in excellent agreement with recent experimental data.
21 citations
TL;DR: In this article, it was shown that the (three-dimensional) tetragonal to orthorhombic transition in the 1-2-3 superconducting compound can be mapped onto a two-dimensional lsing model with anisotropic second neighbor effective pair interactions.
Abstract: It is shown that the (three-dimensional) tetragonal to orthorhombic transition in the 1-2-3 superconducting compound can be mapped onto a two-dimensional lsing model with anisotropic second neighbor effective pair interactions. The Cluster Variation Method (CVM) has been used to calculate a phase diagram based on interaction parameters provided by first principles linear muffin-tin orbital-atomic sphere approximation (LMTO-ASA) calculations performed by P. Sterne at Lawrence Livermore National Laboratory. At high temperature, agreement with experimental phase transition data is excellent. At low temperatures, two-dimensional ordering gives way to quasi one-dimensional states of order as described by the linear chain Ising model for which the thermodynamics are known exactly. Structures produced by Monte Carlo simulation and theoretical diffraction patterns are in striking agreement with recent experimental results.
16 citations
TL;DR: In this paper, it was shown that the (three-dimensional) tetragonal to orthorhombic transition in the 1-2-3 superconducting compound can be mapped onto a two-dimensional Ising model with anisotropic second neighbor effective pair interactions.
Abstract: It is shown that the (three-dimensional) tetragonal to orthorhombic transition in the 1-2-3 superconducting compound can be mapped onto a two-dimensional Ising model with anisotropic second neighbor effective pair interactions. The cluster variation method (CVM) has been used to calculate a phase diagram based on interaction parameters provided by first principles linear muffin-tin orbital-atomic sphere approximation (LMTO-ASA) calculations performed by P. Sterne at Lawrence Livermore National Laboratory. At high temperature, agreement with experimental phase transition data is excellent. At low temperatures, two-dimensional ordering gives way to quasi one-dimensional states of order as described by the linear chain Ising model for which the thermodynamics are known exactly. Structures produced by Monte Carlo simulation and theoretical diffraction patterns are in striking agreement with recent experimental results.
16 citations
TL;DR: In this paper, the authors present an elementary treatment of the essential features of the Cluster Variation Method (CVM) rather than a comprehensive review, and present a tutorial on the CVM in phase diagram calculations.
Abstract: I was asked by the Workshop organizers to write a tutorial on the Cluster Variation Method (CVM) in phase diagram calculations. Hence I shall present an elementary treatment of the essential features of the method rather than a comprehensive review.
14 citations
References
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TL;DR: In this paper, the authors studied the energetic, kinetic and structural properties of hydrogen chemisorbed on a Pd(100) surface by means of thermal desorption, work function and LEED measurements.
345 citations
TL;DR: In this article, the phase diagrams of Ising antiferromagnets in a magnetic field were investigated for various values of the ratio $R$ between nearest-and next-nearest-neighbor interaction.
Abstract: The phase diagrams of Ising antiferromagnets in a magnetic field $H$ are investigated for various values of the ratio $R$ between nearest- and next-nearest-neighbor interaction. While meanfield approximations and the existing real-space renormalization-group treatments yield phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained from Monte Carlo calculations. For $Rl0$ only an antiferromagnetically ordered phase exists. Its transition to the disordered phase is first order for temperatures below the tricritical point (${T}_{t}$,${H}_{t}$). For $R\ensuremath{\rightarrow}0$ also ${T}_{t}\ensuremath{\rightarrow}0$. For $R=0$ we find very good agreement with the results of M\"uller-Hartmann and Zittartz. For $Rg0$ and ${H}_{1}lHl{H}_{2}$ a new phase with anomalous high ground-state degeneracy is found (two sublattices have only one-dimensional order). These sublattices undergo order-disorder transitions at $T=0$, such that for $Tg0$ one is left with a "superantiferromagnetic" phase. At low temperatures in this phase a pronounced tendency is observed to form a simpler (2 \ifmmode\times\else\texttimes\fi{} 2) superstructure but with many antiphase domain boundaries. For $R\ensuremath{\rightarrow}\frac{1}{2}$ and $Hl{H}_{1}$ the regime of the antiferromagnetic phases goes to zero temperature, while for $Rg\frac{1}{2}$ the superantiferromagnetic phase exists also for $Hl{H}_{1}$. The order-disorder transition associated with this phase seems to have non-Ising critical exponents which vary as a function of $R$ and $H$. Estimates for the exponents lead us to suggest that Suzuki's "weak universality" is valid. The behavior of the model at $T=0$ is related to known results on hard-core lattice gases. It is shown that it is useful to interpret the transitions at $T=0$ as generalized percolation transitions. Since the model may have applications to adsorbate phases in registered structures at (100) surfaces of cubic crystals, the transcription of our results to temperature-coverage phase diagrams and adsorption isotherms is discussed in detail, and possible experimental applications are mentioned.
341 citations
TL;DR: In this article, a transformation for a triangular lattice in the space of Ising-spin hamiltonians with short-range forces was constructed and evidence was presented that this transformation exhibits a fixed point corresponding to a hamiltonian with dominant nearest-neighbour interaction.
218 citations
TL;DR: In this paper, the authors present a detailed survey of many samples conducted in two similar but independent calorimeters: the fractional coverages ranged from 5 to 115% of a completed first layer and the temperature range extended from 0.04 to above 10 m\ifmmode^\circ\else\text degree\fi{} K.
Abstract: Heat capacities of ${\mathrm{He}}^{3}$ and ${\mathrm{He}}^{4}$ monolayers adsorbed on "Grafoil" graphite substrates at low temperatures are qualitatively different from previous results using other adsorbents. The present study consists of a detailed survey of many samples conducted in two similar but independent calorimeters: the fractional coverages ranged from 5 to 115% of a completed first layer and the temperature range extended from 0.04 to above 10\ifmmode^\circ\else\textdegree\fi{} K. Several distinct thermodynamic regimes are seen, some of which correspond closely with well-known theoretical models as well as others that had not been predicted. At moderate densities and temperatures the behavior resembles that of two-dimensional gases. Departures from ideality are correlated with quantum-mechanical virial corrections for interacting molecules. In this range of coverages the ${\mathrm{He}}^{4}$ specific heats begin to rise at $T\ensuremath{\lesssim}{3}^{\ensuremath{\circ}}$ K, forming strong rounded peaks near 1\ifmmode^\circ\else\textdegree\fi{}K. ${\mathrm{He}}^{3}$, on the other hand, shows a monotonic decrease with falling temperature until $T\ensuremath{\simeq}{0.2}^{\ensuremath{\circ}}$ K, then (for a narrow range of coverages) reversing the trend to form rounded maxima near 100 m\ifmmode^\circ\else\textdegree\fi{}K. At the lowest temperatures the ${\mathrm{He}}^{3}$ appears to enter a two-dimensional ($2D$) Fermi-liquid regime. At higher coverage both ${\mathrm{He}}^{3}$ and ${\mathrm{He}}^{4}$ undergo second-order phase transitions to regular arrays in registry with the substrate. In the critical region that heat capacities have symmetric peaks of logarithmic shape, with coefficients in close quantitative agreement with exact $2D$ Ising models. Above critical density the ordering peaks disappear and $2D$ liquid and solid behavior is seen. ${\mathrm{He}}^{4}$ at high density and low $T$ is Debye-like, with characteristic temperatures ${\ensuremath{\Theta}}_{2D}$ equal to ${\ensuremath{\Theta}}_{3D}$ of hcp solid ${\mathrm{He}}^{4}$ of the same interatomic spacing. At higher $T$ the $2D$ solid appears to transform to a $2D$ fluid by a continuous process, and pronounced heat-capacity peaks associated with the transformation are located at temperatures near the melting points of hcp ${\mathrm{He}}^{4}$ having the same interatomic spacing. At very low coverage the $2D$ gas character gives way to a regime resembling a low-density $2D$ solid.
208 citations
TL;DR: In this paper, the effect of additional three-body forces and third nearest neighbor forces on the adsorption of hydrogen on Pd(100) was studied. But the effect on the results was not analyzed.
145 citations