The dimer partition function

TL;DR

This paper investigates the dimer problem using the Ginzburg criterion, revealing the upper critical dimension and phase transition behavior, and discusses limitations of the applied approximation.

Contribution

It applies the Ginzburg criterion to resolve contradictions in the dimer problem and clarifies the system's critical dimension and phase transition nature.

Findings

Upper critical dimension is D_{cr}=6

For D≤4, the system undergoes a first order phase transition

The approximation used has limitations leading to some incorrect results

Abstract

We apply the Ginzburg criterion to the dimer problem and we solve the apparent contradiction of a system with mean field $\alpha={1\over2}$, 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.