Statistics of Two-Dimensional Amorphous Lattice

概要

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Statistics of a certain two-dimensional amorphous lattice is investigated. The model is a spatially random lattice constructed by closely packing the plane with equilateral triangles and squares (triangular-square lattice). When the ratio between the number of triangles and squares is varied, the lattice changes continuously from the regular lattice to the square lattice through various kinds of amorphous lattices. By assigning proper Boltzmann weights to triangles and squares, one can define a statistical mechanics of the triangular-square lattice. It is shown that this model can be mapped onto the bond dilution problem on the triangular lattice if a certain restriction is imposed on the way of bond dilution. Making use of this equivalence and thee transfer matrix method, equations of state for semi-infinite systems are calculated exactly by the numerical method. It is shown that the model exhibits most probably a strong first-order transition in the limit of infinite system which corresponds to the solid-liquid transition. The configurational entropy of the amorphous state is also evaluated.
理論物理学刊行会の論文
1983-08-25