Analytic studies of the Yvon-Born-Green equation have suggested that it may show no true critical region for spatial dimension $d<~4$ but that for $d>4$ there is a critical point of the mean-field type. Presented here are the results of numerical solution of the equation which strongly support these suggestions. Thus the Yvon-Born-Green equation exhibits the correct borderline dimensionality of four and the expected mean-field behavior for $d>~4$, but for $d<4$ has only a region of long, but finite, ranged correlations.
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Jones et al. (1982) studied this question.
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