Monte Carlo study of dimer adsorption at monolayer on square lattices

The localized monolayer adsorption of interacting homonuclear dimers (AA) on square lattices is studied using a lattice-gas model. The effect of lateral interactions on the behavior of different thermodynamic quantities is considered. Phase diagrams (i.e. critical temperature versus coverage) are calculated using Monte Carlo simulation and finite-size scaling for both attractive and repulsive nearest-neighbors lateral interactions. Of special interest is the repulsive case where different ordered structures are observed, confirming the results given by Phares et al. [J. Phys. A: Math. Gen. 26 (1993) 6847] based upon exact transfer-matrix method for dimers on a semi-infinite square lattice.

[1]  W. Saam.  Phase transitions in multilayer films , 1983 .

[2]  W. Steele.  The interaction of gases with solid surfaces , 1974 .

[3]  R. Fowler,et al.  An attempt to extend the statistical theory of perfect solutions , 1937 .

[4]  S. Ostlund,et al.  Structural transitions between epitaxially ordered phases in adsorbed submonolayers , 1980 .

[5]  M. W. Cole,et al.  Physical Adsorption: Forces and Phenomena , 1997 .

[6]  K. Binder.  Monte Carlo methods in statistical physics , 1979 .

[7]  R. B. McQuistan,et al.  Exact Occupation Statistics for One-Dimensional Arrays of Dumbbells , 1967 .

[8]  F. A. Putnam,et al.  Renormalization-group treatment of a Potts lattice gas for krypton adsorbed onto graphite , 1978 .

[9]  A. Patrykiejew.  Monte Carlo study in physical adsorption II: A comparison of Monte Carlo and renormalization group results for localized monolayer adsorption on a triagular lattice , 1986 .

[10]  M. Fisher.  Statistical Mechanics of Dimers on a Plane Lattice , 1961 .

[11]  John F. Nagle,et al.  New Series-Expansion Method for the Dimer Problem , 1966 .

[12]  Kurt Binder,et al.  Applications of Monte Carlo methods to statistical physics , 1997 .

[13]  D. E. Shaw,et al.  An approximate solution of the monomer–dimer problem on a square lattice. II , 1985 .

[14]  F. Wunderlich,et al.  Thermodynamics and molecular freedom of dimers on plane triangular lattices , 1986 .

[15]  J. Kosterlitz.  Ordering in Two Dimensions , 1980 .

[16]  A. J. Ramirez-Pastor,et al.  Surface diffusion of dimers: I repulsive interactions , 1997 .

[17]  K. Binder.  Finite size scaling analysis of ising model block distribution functions , 1981 .

[18]  K. Binder,et al.  Multicritical phenomena at surfaces , 1976 .

[19]  F. Wunderlich,et al.  Thermodynamics of dimers on a rectangular L×M×N lattice , 1985 .

[20]  A. Beerbower,et al.  In: Films on Solid Surfaces , 1976 .

[21]  P. W. Kasteleyn.  The statistics of dimers on a lattice: I. The number of dimer arrangements on a quadratic lattice , 1961 .

[22]  Alan M. Ferrenberg,et al.  Critical behavior of the three-dimensional Ising model: A high-resolution Monte Carlo study. , 1991, Physical review. B, Condensed matter.

[23]  S. Ostlund,et al.  Multicritical Phase Diagram of Gases Adsorbed on Graphite: Temperature Variation and Finite-Size Effects , 1979 .

[24]  R Gomer.  Diffusion of adsorbates on metal surfaces , 1990 .

[25]  Kurt Binder,et al.  Monte Carlo Simulation in Statistical Physics , 1992, Graduate Texts in Physics.

[26]  Vladimir Privman,et al.  Finite Size Scaling and Numerical Simulation of Statistical Systems , 1990 .

[27]  F. J. Wunderlich,et al.  Thermodynamics and molecular freedom of dimers on plane honeycomb and Kagomé lattices , 1988 .

[28]  The occupation statistics for indistinguishable dumbbells on a 2×2×N lattice space , 1983 .

[29]  Klein,et al.  Exact enumeration of long-range-ordered dimer coverings on the square-planar lattice. , 1990, Physical review. B, Condensed matter.

[30]  P. W. Kasteleyn.  Dimer Statistics and Phase Transitions , 1963 .

[31]  P. Flory.  Thermodynamics of High Polymer Solutions , 1941 .

[32]  Feibelman.  Rebonding effects in separation and surface-diffusion barrier energies of an adatom pair. , 1987, Physical review letters.

[33]  J. Walker,et al.  Phase diagram of the triangular Ising model: Renormalization-group calculation with application to adsorbed monolayers , 1977 .

[34]  Frenkel,et al.  Nonperiodic solid phase in a two-dimensional hard-dimer system. , 1991, Physical review letters.

[35]  F. Wunderlich,et al.  Structural ordering of interacting dimers on a square lattice , 1993 .

[36]  R. B. McQuistan.  Exact occupation statistics for one-dimensional arrays ofλ-bells , 1968 .

[37]  L. Duenkel,et al.  Topics in Current Physics , 1991 .

[38]  F. Wunderlich,et al.  The entropy curves for interacting dimers on a square lattice , 1993 .

[39]  K. Binder.  Finite size effects at phase transitions , 1992 .

[40]  Elliott H. Lieb,et al.  Solution of the Dimer Problem by the Transfer Matrix Method , 1967 .

[41]  A. Phares.  The occupation statistics for indistinguishable dumbbells on a rectangular lattice space. I , 1984 .

[42]  M. Fisher,et al.  Dimer problem in statistical mechanics-an exact result , 1961 .

[43]  J. G. Dash,et al.  Phase Transitions in Surface Films , 1980 .

[44]  D. S. Gaunt,et al.  Exact Series-Expansion Study of the Monomer-Dimer Problem , 1969 .