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In a previous article, we develop a continuous version of Kasteleyn theory tostudy the bead model on the torus. These are the point processes on thesemi-discrete torus $\mathbb{T}_n := [0,1) \times \{0,1,\ldots,n-1\}$ (thoughtof as $n$ unit length strings wrapped around a doughnut) with the property thatbetween every two consecutive points on same string, there lies a point on theneighbouring strings. In this companion article, we obtain the main results ofthe previous article via an alternative route, using scaling limits of dimermodels as opposed to the continuous Kasteleyn theory. In any case, we hope thatthe article may serve as a gentle introduction to Kasteleyn theory on thetorus.

Beads on the torus via scaling limits of dimer matchings