WHY IS CV LESS SINGULAR THAN CP NEAR 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 CV 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 CV 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. © 1969 The American Physical Society.