Determination of the theoretical parameters

The theory involves four parameters related to the use of low order perturbation theory  

One of these parameters can be fixed arbitrarily. This is due to the two-parameter nature of the theory which guarantees that the renormalized variables occur only in the combination, q2N ) cprN [2, corresponding 

The choice of no governs r for small momenta in the dilute limit where Eq. (13.21) reduces to Nr = no- We thus should consider some universal ratio, defined for c — 0, q -+ 0 which must be most sensitive to Nr. The interpenetration ratio ip is a good candidate, since it depends on Nr even in zero-loop approximation. From Sect. 15.4, Eq, (15.54) we take the one-loop order result 

A similar determination of Co or qo based on appropriate critical ratios is presented in Appendix A 13.2. Summarizing the results we choose the theoretical parameters as 

The resulting value of u (Eq, (13,18)) is u — 8.107, It must be stressed that the parameter values (13.22) are adjusted to a one-loop evaluation of the scaling functions within the present formulation of renormalized perturbation theory in d — 3 and would have to be readjusted if for instance we would work to two-loop order. 

The formal argument is given in Appendix A 13. L We exploit this freedom to dioose 6iji(l) = 1. The remaining parameters can be seen to govern the crossover in temperature (no), overlap (co) or momentum (go)- We exemplify the choice of these parameters with no. 

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