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Efficient Algorithms for the Two-Dimensional Ising Model with a Surface Field

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Abstract

The bond propagation and site propagation algorithms are extended to the two-dimensional (2D) Ising model with a surface field. With these algorithms we can calculate the free energy, internal energy, specific heat, magnetization, correlation functions, surface magnetization, surface susceptibility and surface correlations. The method can handle continuous and discrete bond and surface-field disorder and is especially efficient in the case of bond or site dilution. To test these algorithms, we study the wetting transition of the 2D Ising model, which was solved exactly by Abraham. We can locate the transition point accurately with a relative error of \(10^{-8}\). We carry out the calculation of the specific heat and surface susceptibility on lattices with sizes up to \(200^2 \times 200\). The results show that a finite jump develops in the specific heat and surface susceptibility at the transition point as the lattice size increases. For lattice size \(320^2 \times 320\) the parallel correlation length exponent is \(1.86\), while Abraham’s exact result is \(2.0\). The perpendicular correlation length exponent for lattice size \(160^2\times 160\) is \(1.05\), whereas its exact value is \(1.0\).

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Acknowledgments

The author thanks J. O. Indekeu for useful discussions.

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  1. Department of Physics, Beijing Normal University, Beijing, 100875, China

    Xintian Wu

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Wu, X. Efficient Algorithms for the Two-Dimensional Ising Model with a Surface Field. J Stat Phys 157, 1284–1300 (2014). https://doi.org/10.1007/s10955-014-1109-5

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  • DOI: https://doi.org/10.1007/s10955-014-1109-5

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