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The Breaking of Geometric Constraint of Classical Dimers on the Square Lattice

2021/06/17 by Hongxu Yao, Yao, Hongxu, Jiaze Li +3
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Mathematics and Applications #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2106.09674

openalex publication_date 2021/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a model of two-dimensional classical dimers on the square lattice with strong geometric constraints (there is exactly one bond with the nearest point for every point in the lattice). This model corresponds to the quantum dimer model suggested by D.S. Rokhsar and S.A. Kivelson (1988). We use the directed-loop algorithm to show the system undergoes a Berezinskii-Kostelitz Thousless transition (BKT transition) in finite temperatures. After that, if we destroy the geometric constraint of dimers, the topological transition will transfer to a quasi one-order transition. For the dimer updates, we also introduce a new cluster updating algorithm called the edged cluster algorithm. By this method, we succeed in rapidly traversing the winding (topological) sections uniformly and widening the effective matrical ensemble to include more topological sections.

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