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Tensor renormalization group study of hard-disk models on a triangular lattice

Akimenko, S. S., Gorbunov, V. A., Myshlyavtsev, A. V. and Stishenko, P. V. 2019. Tensor renormalization group study of hard-disk models on a triangular lattice. Physical Review E 100 (2) , 022108. 10.1103/PhysRevE.100.022108

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Abstract

High accuracy and performance of the tensor renormalization group (TRG) method have been demonstrated for the model of hard disks on a triangular lattice. We considered a sequence of models with disk diameter ranging from a to 2√3a, where a is the lattice constant. Practically, these models are good for approximate description of thermodynamics properties of molecular layers on crystal surfaces. Theoretically, it is interesting to analyze if and how this sequence converges to the continuous model of hard disks. The dependencies of the density and heat capacity on the chemical potential were calculated with TRG and transfer-matrix (TM) methods. We benchmarked accuracy and performance of the TRG method comparing it with TM method and with exact result for the model with nearest-neighbor exclusions (1NN). The TRG method demonstrates good convergence and turns out to be superior over TM with regard to considered models. Critical values of chemical potential (μc) have been computed for all models. For the model with next-nearest-neighbor exclusions (2NN) the TRG and TM produce consistent results (μc=1.75587 and μc=1.75398 correspondingly) that are also close to earlier Monte Carlo estimation by Zhang and Deng. We found that 3NN and 5NN models shows the first-order phase transition, with close values of μc (μc=4.4488 for 3NN and 4.4<4.5 for 5NN). The 4NN model demonstrates continuous yet rapid phase transition with 2.65<2.7.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Chemistry
Publisher: American Physical Society
ISSN: 2470-0045
Last Modified: 04 Oct 2021 15:15
URI: https://orca.cardiff.ac.uk/id/eprint/143483

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