L-shape NLCE expansion for square-lattice models

We introduce a Numerical Linked Cluster Expansion (NLCE) based on L-shaped clusters in the square lattice. NLCE expansions are known to converge – exponentially fast in the size of the clusters – in unordered phases. In ordered phases, even if the correlation length is finite (such as in the classical Ising model in the square lattice), NLCE expansions based on bonds or sites fail to converge. We show that the expansion proposed in this study, however, converges (exponentially fast in the size of the clusters) as one approaches the ground state of the classical Ising model and the transverse field Ising model. Furthermore, we show that studying thermodynamic properties of those models below and above the transition allows us to bound the critical region in which the phase transition occurs.