Abstract
We apply the singular value decomposition method to matrices made from eigenvectors of the transfer matrix of a 19-vertex model on a square lattice with full frustration. The conformal anomaly c is estimated to be close to 3/2. This result suggests that the 19-vertex model with full frustration has a single transition due to two kinds of degrees of freedom, each of which has U(1) symmetry and ${Z}_{2}$ symmetry. Moreover, we find that the value of index $\ensuremath{\eta}$ is smaller than that at the Berezinskii-Kosterlitz-Thouless (BKT) transition by considering a logarithmic correction to the finite size analysis. This result for $\ensuremath{\eta}$ suggests that there is another universality class which is different from that of either the Onsager type or the BKT type.
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