Transfer matrix test of the two-cell mean-field renormalization group

A transfer matrix approach has been worked out to test the predictions of the two-cell mean-field renormalization group (MFRG) for the square Ising cells with linear size up to L 11. The convergence of the finite-size critical couplings towards the exact value both for MFRG and for the cluster MFA is shown and the limit of the ratio yh/yt consistent with the corresponding universal value is found. Applications within MFA are also briefly discussed