CRITICAL BEHAVIOR OF AN ANHARMONIC NANOSCOPIC SOLID

The paper presents a toy model of phase transition in an anharmonic solid. The starting point of our study is a 2D or 3D rectangular lattice of on-site quantum quartic oscillators, interacting with their nearest neighbors by elastic forces. The critical equation of the order-disorder transition is obtained using the theory of dielectric susceptibility. To obtain a mathematically tractable model, the quartic potential a symmetric, two well potential - is replaced by a similar, but more workable one - a rectangular symmetric two well potential. For energies and wave functions corresponding to the lowest states, we obtain accurate analytical approximations, which lead to a simple critical equation. It gives the critical temperature as a function of the anhar-monicity of potential. Similar toy models can be obtained using other workable, two well potentials. Applications in nanophysics are briefly discussed.

Automated summary

The paper introduces a toy model for studying phase transition in an anharmonic solid by utilizing a 2D or 3D lattice structure with quantum quartic oscillators interaction. By replacing the anharmonic quartic potential with a more workable rectangular two well potential, an analytical critical equation is obtained. Applications in nanophysics are briefly mentioned.