An approximate solution of the monomer-dimer problem on a square lattice. II.
The mathematical method developed in paper I is applied to obtain the partition function and thermodynamical properties of the monomer–dimer problem for a square lattice in terms of the absolute activity x. We also obtain by extrapolation an approximate expression of the partition function which is accurate to better than 0.1% in the range 0≤x≤10. The expectation of the statistics 〈θ(x)〉 is calculated in two different ways and numerical results agree to better than 3%, thus showing the consistency of the underlying mathematical method. Consistent with earlier studies, there is no phase transition. Approximation methods used in earlier work are also found to be in good agreement with our analytic study.
|Main Author:||Phares, Alain J.|
|Other Authors:||Shaw, Donald E., Wunderlich, Francis J.|