Observations on the criticality of the Yvon-Born-Green equation of state

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Abstract
Recent analyses of the Yvon-Born-Green equation strongly suggest that if it has a critical point, the critical correlations are, for spatial dimension less than four, negative at long range. We present here new numerical evidence that the YBG equation, in spatial dimension three, does not have a critical point, in contrast to the conclusions reached in previous numerical work. Our evidence comes from new numerical solutions which are closer to the supposed critical point and of greater precision than was achieved in the previous work. The extrapolations inferred from the previous work are not followed by the new solutions. The conclusion that there is no true critical point is based on three observations. (1) None of our numerical solutions are negative at long range. (2) The inverse compressibility does not extrapolate to zero along any isochore in the vicinity of the supposed critical point. (3) The inverse correlation length does not extrapolate to zero in the vicinity of the critical point, but rather goes through a nonzero minimum at a point of maximum, but not infinite, correlation length.