Extended Ising Model Research Articles

Site correlation as a means to determine interactions between adsorbed atoms on metal (100) surfaces

The probabilities of nn and nnn pairs are calculated for an extended Ising model on the sq lattice. Dominant nn repulsion and an arbitrary nnn interaction are considered in order to model the most usual cases of adsorbed gases on (100) metal surfaces. The results are displayed in a way so as to permit a simple and reliable determination of the interaction parameters between nearest and next nearest neighbours from experimentally determined values of nn and nnn correlations. It turns out that for the determination of interactions the surface concentration range around c s = 0.25 is most suitable.

Adsorption of interacting atoms to (100) surfaces model calculations: hard core at nn and finite interactions up to third neighbor distance

Some species of atoms adsorbing to (100) surfaces of metals show a very strong repulsion at nearest neighbor (nn) position and finite interactions over larger distances. In this contribution adsorption isotherms are calculated for the case of infinitely strong nn repulsion, finite second neighbor repulsion and third neighbor attraction using an extended Ising model on a periodic lattice of 50×50 sites. They show the typical behavior corresponding to mixed interactions. Although the detailed discussion of critical phenomena is postponed, a tricritical point emerges where the phase transitions change from second to first order. Moreover within a certain parameter range the isotherms show an unusual asymmetry between the low-cs (cs < 0.25) and the high-cs (0.25 <cs < 0.5) part closely resembling experimental equilibrium adsorption isotherms for O/Ni(100). From the comparison between theory and experiment values for the oxygen interaction potentials on Ni(100) are deduced.

On the equilibrium segregation of interacting impurity atoms towards (100) metal surfaces: I. Theoretical considerations including first- and second-neighbor interactions

Experiments on the segregation of foreign atoms towards single crystal surfaces usually show long-range-order phenomena and/or strong deviations from the Gihbs-McLean behavior both indicating the presence and importance of interactions between the segregating atoms. Model calculations of segregation bulk isosteres for interacting impurity atoms segregating towards (100) metal surfaces are therefore presented based on an extended Ising model using the Monte Carlo method. Interactions between nearest and next-nearest neighbors are considered and bulk isosteres given for a number of combinations of values thereof. In a paper to follow the results of these calculations are to be applied to existing experiments and values for certain interaction enthalpies deduced.

Triplet interactions and the c(2×2) overlayer phase diagram

Abstract Square lattice phase diagrams are investigated with the extended Ising model, considering pair and triplet interactions. We determine the stability of the c(2×2) structure as a function of different triplet interactions. A systematical study of the asymmetry of the phase diagram shows that the triplet interactions with two nnn bounds play a major role in producing an asymmetric phase diagram. The experimental phase diagram of hydrogen adsorbed on a Pd (001) surface is discussed within this framework.

Extended Ising model.

In this paper we describe a numerical method of solving the local-density mean-field equations of spatially frustrated lattice models. Using techniques of simulated annealing and simultaneous updating of collective modes, we have been able to locate the global minima of a function with many nearby local minima. This approach is applied to an isotropic frustrated lattice model with magnetic field in order to determine the global phase diagram. We also mention a related simulation technique which might be used to replace the traditional single-spin-flip Monte Carlo method. This appears to be a promising way of simulating periodic spatially frustrated lattice Hamiltonians. Finally, some consideration is given to the physical interpretation of a lattice model of microemulsions.

Theorems on Extended Ising Model with Applications to Dilute Ferromagnetism

It is proved that the zeros of the partition function of an extended Ising model lie on a unit circle in the fugacity piane under certain conditions. Each spin assumes a general value. The key point of the proof is to derive a simple condition sufficient for zeros of polynomials to lie on a unit circle. Conjectured theorems on the Heisenberg model are also discussed.