EXTRAPOLATION-CAM THEORY FOR CRITICAL EXPONENTS

摘要

We propose and test a new method for generating canonical sequences for analysis by the coherent anomaly method (CAM) from non-mean-field approximations. By intentionally underestimating the rate of convergence of exact-diagonalization values for the mass or energy gaps of finite systems, we form families of sequences of gap estimates. The gap estimates cross zero with generically nonzero linear terms in their Taylor expansions, so that nu = 1 for each member of these sequences of estimates. Thus, the CAM can be used to determine nu. Our freedom in deciding exactly how to underestimate the convergence allows us to choose the sequence that displays the dearest coherent anomaly. We demonstrate this approach on the two-dimensional ferromagnetic Ising model, for which nu = 1. We also use it on the three-dimensional ferromagnetic Ising model, finding nu approximate to 0.629, in good agreement with other estimates. Finally, we apply it to an antiferromagnetic spin-1 Heisenberg chain, finding nu approximate to 0.987 at the phase transition between the Haldane phase and the dimerized phase, in agreement with the field-theoretic prediction nu = 1. Although the specific systems used to test the extrapolation-CAM procedure involve finite system sizes, the method could be applied to other finite approximations, such as systematic variational approximations. [References: 33]