A Note on Thermodynamics of the Frenkel-Kontorowa Systems in High-Temperature Regions: Comparison with the Exact Solutions of Schneider-Stoll

Abstract

The lowest eigenvalue of the transfer-integral equation for the Frenkel-Kontorowa system, having the misfit parameter l (closely related to a normalized particle density ρ), and the specific heat derived therefrom are analytically discussed from a high-temperature expansion approach. In the case of l=0 (ρ=1) for which Schneider-Stoll [SS] have obtained exact numerical solutions, we can reproduce a maximum of the specific heat about 1.06 at k_BT=11.0 in SS units, being passably consistent with the SS exact result. The cases for l≠0 (1>ρ>0.5) are also studied together with a validity range of the present approximation.