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Charles M. Newman studied critical behavior in percolation with Michael Aizenman. Their tree-diagram inequalities bound multipoint connection probabilities using two-point functions. A diagrammatic convergence criterion gives mean-field behavior for the percolation susceptibility exponent, connecting the geometry of large clusters with quantitative critical scaling.^[ref]

By Michael Aizenman, Charles M. Newman.

Journal of Statistical Physics 36(1–2), 107–143. Author/institutional record collaborate.princeton.edu/en/publications/tree-graph-inequalities-and-critical-behavior-in-percolation-mode/ confirms diagrammatic convergence criterion for susceptibility exponent gamma=1.