Critical Behavior of Ferromagnetic Ising Model on Triangular Lattice

Abstract

We apply a new updating algorithm scheme to investigate the critical behavior of the two-dimensional ferromagnetic Ising model on a triangular lattice with nearest neighbour interactions. The transition is examined by generating accurate data for large lattices with $L=8,10,12,15,20,25,30,40,50$. The spin updating algorithm we employ has the advantages of both metropolis and single-update methods. Our study indicates that the transition to be continuous at $T_c=3.6403(2)$. A convincing finite-size scaling analysis of the model yield $\nu =0.9995(21)$, $\beta /\nu =0.12400(18)$, $\gamma /\nu =1.75223(22)$, ${\gamma }^{\prime }/\nu =1.7555(22)$, $\alpha /\nu =0.00077(420)$ (scaling) and $\alpha /\nu =0.0010(42)$(hyperscaling) respectively. Estimates of present scheme yield accurate estimates for all critical exponents than those obtained with Monte Carlo methods and show an excellent agreement with their well-established predicted values.

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