V. I. Tokar — Page 2

arXiv2002

Analytical solution of 1D lattice gas model with infinite number of multiatom interactions

We consider a 1D lattice gas model in which the atoms interact via an infinite number of cluster interactions within contiguous atomic chains plus the next nearest neighbor pairwise interaction. All interactions are of arbitrary strength. An analytical expression for the size distribution of atomic chain lengths is obtained in the framework of the canonical ensemble formalism. Application of the exact solution to the problems of self-assembly and self-organization is briefly discussed.

cond-mat.mtrl-sci↗

arXiv2002

Lattice gas models of coherent strained epitaxy

The harmonic Frenkel-Kontorova model is used to illustrate with an exactly solvable example a general technique of mapping a coherently strained epitaxial system with continuous atomic displacements onto a lattice gas model (LGM) with only discrete variables. The misfit strain of the original model is transformed into cluster interatomic interactions of the LGM. The clusters are contiguous atomic chains of all lengths but the interaction strength for long chains is exponentially small. This makes possible the application of efficient Monte Carlo techniques developed for discrete variables both in kinetic and equilibrium simulations. The formalism developed can be applied to 1D as well as to 2D systems. As an illustrative example we consider the problem of self-organization of 1D size calibrated clusters on the steps of the vicinal surfaces.

cond-mat.mtrl-sci↗