# Order of Limits using Replica Trick

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I'm trying to use the replica trick ($Z\rightarrow Z^{n})$ to evaluate a particular partition function (over an $N\times N$ matrix), and I've hastily assumed that I can commute the limits of $N\rightarrow \infty$ and $n\rightarrow 0$, but upon further reflection I realize this may not be true. What conditions must be satisfied for these limits to be interchangeable?

asked Dec 21, 2015
edited Dec 21, 2015

the existence of an absolute convergent majorant (cf. dominated convergence and Fubini's theorem).

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