中国物理B ›› 2009, Vol. 18 ›› Issue (7): 2696-2702.doi: 10.1088/1674-1056/18/7/012

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Critical behaviour of the ferromagnetic Ising model on a triangular lattice

罗志环1, 刘岩2, 林健荣3, Loan Mushtaq4   

  1. (1)Department of Applied Physics, South China Agricultural University, Guangzhou 510642, China;Department of Physics, Sun Yet-Sen University, Guangzhou 510275, China; (2)Department of Applied Physics, South China Agricultural University, Guangzhou 510642, China; (3)Engineering College, South China Agricultural University, Guangzhou 510642, China; (4)International School, Jinan University, Guangzhou 510632, China
  • 收稿日期:2008-10-13 修回日期:2008-11-12 出版日期:2009-07-20 发布日期:2009-07-20
  • 基金资助:
    Project supported partially by Guangdong Natural Science Foundation (GDNSF) of China (Grant No 07300793). One of authors (Loan Mushtaq) was partially supported by the Guangdong Ministry of Education, China.

Critical behaviour of the ferromagnetic Ising model on a triangular lattice

Luo Zhi-Huan(罗志环)a)b), Loan Mushtaqc), Liu Yan(刘岩)a)†, and Lin Jian-Rong(林健荣)d)   

  1. a Department of Applied Physics, South China Agricultural University, Guangzhou 510642, China; b Department of Physics, Sun Yet-Sen University, Guangzhou 510275, China; c International School, Jinan University, Guangzhou 510632, China; d Engineering College, South China Agricultural University, Guangzhou 510642, China
  • Received:2008-10-13 Revised:2008-11-12 Online:2009-07-20 Published:2009-07-20
  • Supported by:
    Project supported partially by Guangdong Natural Science Foundation (GDNSF) of China (Grant No 07300793). One of authors (Loan Mushtaq) was partially supported by the Guangdong Ministry of Education, China.

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摘要： We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L= 8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at Tc= 3.6403({2}). A convincing finite-size scaling analysis of the model yields υ=0.9995(21), β / υ = 0.12400({17}), γ / υ = 1.75223(22), γ '/υ=1.7555(22), α/υ= 0.00077(420) (scaling) and α / υ = 0.0010(42) (hyperscaling). The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values.

Abstract: We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L= 8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at Tc = 3.6403(2). A convincing finite-size scaling analysis of the model yields $\nu$ = 0.9995(21), $\beta/\nu$ = 0.12400(17),  $\gamma/\nu$ = 1.75223(22),  $\gamma'/\nu$ = 1.7555(22), $\alpha/\nu$= 0.00077(420) (scaling) and $\alpha/\nu$ = 0.0010(42) (hyperscaling). The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values.

Key words: Ising model, triangular lattice, Monte Carlo method

中图分类号:  (Classical spin models)

  • 75.10.Hk
05.50.+q (Lattice theory and statistics) 75.40.Mg (Numerical simulation studies) 75.40.Cx (Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.))