Critical behaviour of the ferromagnetic Ising model on a triangular lattice

We use a new updated algorithm scheme to investigate the criticalbehaviour of the two-dimensional ferromagnetic Ising model on atriangular lattice with the nearest neighbour interactions. Thetransition is examined by generating accurate data for lattices with$L = 8$, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spinalgorithm we employ has the advantages of both a Metropolis algorithmand a single-update method. Our study indicates that the transition iscontinuous at $T_{rm c} = 3.6403({2})$. A convincing finite-sizescaling 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 moreaccurate estimates for all the critical exponents than the Monte Carlomethod, and our estimates are shown to be in excellent agreementwith their predicted values.