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Note that our definition of τ and the cutoff function in eq 2 is different from that used in eqs 6.118 and 6.122 in ref 25. In the latter two equations, the number density for HBPs is written as n(N, N -2(N/Nchar)2-τf (N/Nchar, N-τFf̃ (N/Nchar, where τF, 2 is the Fisher exponent and f̃ (N/Nchar, N/Nchar) 2-τf (N/Nchar) is a modified cutoff function which contains a power law in N/Nchar. The two forms for n(N) are obviously equivalent. In this paper, we choose to work with the form given by eq 2 since we prefer to work with a cutoff function that has no hidden power law scaling
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char. The two forms for n(N) are obviously equivalent. In this paper, we choose to work with the form given by eq 2 since we prefer to work with a cutoff function that has no hidden power law scaling.
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