Toroidal Dimer Model and Temperley's Bijection

Wangru Sun

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arXiv · 1603.00690

Toroidal Dimer Model and Temperley's Bijection

Wangru Sun

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Abstract

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

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Wangru Sun. 2016-03-02. Toroidal Dimer Model and Temperley's Bijection. https://arxiv.org/abs/1603.00690

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