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Temperley's bijection relates the toroidal dimer model to cycle rootedspanning forests ($CRSF$) on the torus. The height function of the dimer modeland the homology class of $CRSF$ are naturally related. When the size of thetorus tends to infinity, we show that the measure on $CRSF$ arising from thedimer model converges to a measure on (disconnected) spanning forests orspanning trees. There is a phase transition, which is determined by the averageheight change.

Toroidal Dimer Model and Temperley's Bijection