Alternative transfer-matrix approach to two-dimensional systems with competing interactions in one direction

A transfer-matrix representation in terms of Pauli spin matrices is used to perform a phenomenological renormalization and finite-size scaling analysis of two-dimensional spin models with competing interactions in one direction. This enables us to obtain the leading eigenvalues of the transfer matrix with a significative saving of computer time using the Lanczos scheme. The phase diagrams of the axial next-nearest-neighbor Ising model and a model with competing two- and four-spin couplings in one direction are studied. The order of the phase transitions was determined by examining the finite-size scaling behavior of the persistence length. Data for the normalized scaled persistence length display scaling on the ferromagnetic-paramagnetic transition line for both models.