THE CLE CONDITION AND THE CORRELATION LENGTH ON THE SQUARE LATTICE ISING-MODEL WITH 1ST-NEIGHBOR AND 2ND-NEIGHBOR INTERACTIONS

The square Ising lattice with nearest- and next-nearest-neighbour interactions is considered. On the basis of the simplest ansatz on the principal eigenvector of the transfer matrix of the model and of the CLE condition, developed in previous papers, the correlation length along a column is calculated for all T greater-than-or-equal-to T(c) in the ferromagnetic and antiferromagnetic regions. A comparison is made with results obtained through other methods. For competing interactions, it is shown that there is a mechanism which leads to a correlation length made of two analytic pieces.