Why isCVLess Singular thanCPnear the Critical Point?

The fact noted by Schofield that the specific heat at constant volume, albeit singular, is less singular than the specific heat at constant pressure implies an asymptotic relation between the two-, three-, and four-body distribution functions. The experimental background of this fact is discussed and a fluctuation formula which expresses $C_V$ in terms of two-, three-, and four-body correlation functions is derived. A heuristic explanation of the asymptotic properties of the distribution functions is given based on the fact that local fluctuations proportional to the critical eigenvector are overwhelmingly the most probable near the critical point. It is shown that if $C_V$ is indeed infinite there exists a second critical eigenvector linearly independent of the first. Some consequences of the existence of two critical eigenvectors are discussed, and a form for the short-range behavior of the distribution functions near the critical point is conjectured.