On the classical critical behavior of the specific heat capacity of a model of structural phase transitions with a long-range interaction

Abstract

The critical specific heat capacity c of a d-dimensional model describing structural phase transitions in an anharmonic crystal with a long-range interaction (decreasing at large distances r as r −d−σ , 0 < σ ≤ 2) is studied near the classical critical point Tc . At temperatures T > Tc and for dimensions σ < d < 2σ (σ and 2σ are the lower and the upper critical dimensions, respectively) the critical specific heat capacity is obtained in the form c ≈ 1 − Dεαs , where D > 0 and αs < 0 depend only on the ratio d/σ, and ε = T/Tc −1 is a measure of the deviation from the critical point. For three fixed values of the ratio d/σ the dependence c ≈ c(ε) is graphically presented. It is shown that at all temperatures T ≤ Tc the specific heat capacity retains its maximum value, c max = 1. The critical exponent αs , obtained here, coincides with that of the known mean spherical model, while c max is different for the two models.