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Chin. Phys. B, 2009, Vol. 18(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

Luo Zhi-Huan(罗志环)a)b), Loan Mushtaqc), Liu Yan(刘岩)a)†, and Lin Jian-Rong(林健荣)d)
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
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 T= 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.
Keywords:  Ising model      triangular lattice      Monte Carlo method  
Received:  13 October 2008      Revised:  12 November 2008      Accepted manuscript online: 
PACS:  75.10.Hk (Classical spin models)  
  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.))  
Fund: 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.

Cite this article: 

Luo Zhi-Huan(罗志环), Loan Mushtaq, Liu Yan(刘岩), and Lin Jian-Rong(林健荣) Critical behaviour of the ferromagnetic Ising model on a triangular lattice 2009 Chin. Phys. B 18 2696

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