On the critical specific heat capacity of a classical anharmonic crystal with long-range interaction

Abstract

The bulk critical specific heat capacity of a classical anharmonic crystal with long-range interaction (decreasing at large distances r as r−d−a, where d is the space dimensionality and 0 < σ ≤ 2) is studied. An exact analytical expression is obtained at the upper critical dimension d = 2σ of the system. This result depends on both the deviation from the critical point and the space dimensionality of the system, while the known asymptotic one depends only on the deviation from the critical point. For real systems (chains, thin layers, i.e. films and three-dimensional systems) the exact result and the asymptotic one are graphically presented and compared on the basis of the calculated relative errors. The obtained result holds true in a broader neighborhood of the critical point. The expansion of the critical region is estimated at the three real physical dimensionalities.