Exact solution to the one-and two-dimensional models of the binary lattice with nearest-neighbor interactions (original) (raw)
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The Journal of Chemical Physics, 2001
This work is a generalization of the work of Widom ͓J. Chem. Phys. 39, 2808 ͑1963͔͒ and of Henderson ͓Mol. Phys. 95, 187 ͑1998͔͒. Based on geometric analysis and statistical thermodynamics arguments, a set of sum rules for two-component nearest-neighbor interaction models at thermodynamic equilibrium is derived. By choosing the density of one component and the unlike-bond density 12 as two variables, it is shown that the energy is well-behaved; however, the entropy, s(, 12 ), is independent of within two-phase regions, but not outside. Temperature and chemical potentials determine the equilibrium and 12 . The exact entropy function for 1-D systems can be calculated, and an exact free energy density function is formulated. The result shows that s is always dependent on except at 12 ϭ0, which excludes the possibility of phase transitions at finite temperature.
Thermodynamic studies of the two dimensional Falicov-Kimball model on a triangular lattice
The European Physical Journal B, 2011
Thermodynamic properties of the spinless Falicov-Kimball model are studied on a triangular lattice using numerical diagonalization technique with Monte-Carlo simulation algorithm. Discontinuous metal-insulator transition is observed at finite temperature. Unlike the case of square lattice, here we observe that the finite temperature effect is not able to smear out the discontinuous metal-insulator transition seen in the ground state. Calculation of specific heat (Cv) shows single and double peak structures for different values of parameters like on-site correlation strength (U), f −electron energy (E f) and temperature.
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Journal of Physics A: Mathematical and General, 1998
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Acta Physica Polonica A, 1994
The density series of the non-interacting hard-square lattice gas model are reanalyzed by the ratio, Dlog Pad and differential approximant methods. The problem of poor consistency between series and other results is resolved. Transfer matrix calculations are performed, implementing both finite-size scaling and conformal invariance. Very accurate estimates of the critical exponents y, and yh are obtained in agreement with Ising universality. Furthermore, an improvement of the value of the critical density pc is found. In addition, the universal critical-point ratios of the square of the second and the fourth moment of the magnetization for ferromagnetic Ising models on the square and on the triangular lattice with periodic boundary conditions are reported.
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The Journal of Chemical Physics, 2008
The properties of a simple one-dimensional lattice model with two repulsive ranges are studied in terms of its analytic solution. Its phase behavior is characterized by the presence of a disorder-order-disorder transition ͑or a fluid-solid-fluid transition in lattice gas language͒. A similar situation was discussed by Hemmer and Stell ͓Phys. Rev. Lett. 24, 1284 ͑1970͔͒ when considering the purely repulsive version of their ramp potential. The melting of the solid phase, when pressure is increased along an isotherm, is a feature common to both models and one of the characteristic features of water.
Physica, 1970
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Abstract. For detailed applications of lattice gas models to surface systems, mul-tisite interactions often play at least as significant a role as interactions between pairs of adatoms that are separated by a few lattice spacings. We recall that trio (3-adatom, non-pairwise) interactions do not inevitably create phase-boundary asym-metries about half coverage. We discuss a sophisticated application to an experi-mental system and describe refinements in extracting lattice-gas energies from cal-culations of total energies of several different ordered overlayers. We describe how lateral relaxations complicate matters when there is direct interaction between the adatoms, an issue that is important when examining the angular dependence of step line tensions. We discuss the connector model as an alternative viewpoint and close with a brief account of recent work on organic-molecule overlayers. 1.1
Study Of A Planar Lattice Model With $ P_4 $ Interaction
Arxiv preprint cond-mat/9708131, 1997
A planar square lattice model with 3-d spins interacting with nearest neighbours through a potential-ǫP 4 (cosθ ij) is studied by Monte Carlo technique. Lattice sizes from 10×10 to 30×30 are considered for calculating various thermodynamic averages. A 80×80 lattice has been used to obtain the pair correlation function. To accurately ascertain the order of the phase transition the Ferrenberg-Swendsen technique has been used on a 120×120 lattice. Our study predicts that the system exhibits a first order phase transition which is confirmed by the twin-peaked nature of the distribution function. The pair correlation function shows an algebraic decay at low temperatures and an exponential decay at high temperatures. Mean field and Two-site Cluster calculations have also been performed and the latter is found to predict the thermodynamic averages fairly accurately.