Random trimer tilings

Ghosh, Anandamohan ; Dhar, Deepak ; Jacobsen, Jesper L. (2007) Random trimer tilings Physical Review E, 75 (1). 011115_1-011115_13. ISSN 1063-651X

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Official URL: http://pre.aps.org/abstract/PRE/v75/i1/e011115

Related URL: http://dx.doi.org/10.1103/PhysRevE.75.011115


We study tilings of the square lattice by linear trimers. For a cylinder of circumference m, we construct a conserved functional of the base of the tilings, and use this to block diagonalize the transfer matrix. The number of blocks increases exponentially with m. The dimension of the block corresponding to the largest eigenvalue is shown to grow as (3/21/3)m. We numerically diagonalize this block for m≤27, obtaining the estimate S=0.158520±0.000015 for the entropy per site in the thermodynamic limit. We present numerical evidence that the continuum limit of the model has conformal invariance. We measure several scaling dimensions, including those corresponding to defects of monomers and L-shaped trimers. The trimer tilings of a plane admits a two-dimensional height representation. Monte Carlo simulations of the height variables show that the height-height correlations grows logarithmically at large separation, and the orientation-orientation correlations decay as a power law.

Item Type:Article
Source:Copyright of this article belongs to American Physical Society.
ID Code:9302
Deposited On:02 Nov 2010 12:32
Last Modified:16 May 2016 19:07

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