Bond-propagation algorithm for thermodynamic functions in general two-dimensional Ising models

Recently, we developed and implemented the bond-propagation algorithm for calculating the partition function and correlation functions of random-bond Ising models in two dimensions [ Y. L. Loh and E. W. Carlson Phys. Rev. Lett. 97 227205 (2006)]. The algorithm is the fastest available for calculating these quantities near the percolation threshold. In this paper, we show how to extend the bond-propagation algorithm to directly calculate thermodynamic functions by applying the algorithm to derivatives of the partition function and we derive explicit expressions for this transformation. We also discuss variations of the original bond-propagation procedure within the larger context of Y∇Y reducibility and discuss the relation of this class of algorithm to other algorithms developed for Ising systems. We conclude with a discussion on the outlook for applying similar algorithms to other models.