The dimer partition function

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We apply the Ginzburg criterion to the dimer problem and we solve the apparent contradiction of a system with mean field $α={1\over2}$, the typical value of tricritical systems, and upper critical dimension $D_{cr}=6$. We find that the system has upper critical dimension $D_{cr}=6$ , while for $D\le4$ it should undergo a first order phase transition. We comment on the latter wrong result examining the approximation we used.
6 pages, Latex, NBI-HE-93-16

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