A New Method to Predict Critical Temperature of the Ising Modelby Extrapolating Variational Cumulant Expansion to Infinite Order

The critical temperatures of the Ising model in square and simple cubic lattices are derived with the variational-cumulant expansion approach to the seventh order. An extrapolating method is proposed to predict the critical temperature of infinite series according to the finite order expansion, at which a weighted fitting method is used. For the 2-dimensional Ising model, the critical temperature obtained by this method is in a deviation of 0.04% compared with the exact value, and the estimated results are robust for different order prediction. The critical temperature for the 3D Ising model is predicted as 4.490.