Phase transition for a uniformly frustrated 19-vertex model by use of the density matrix renormalization group

Abstract We investigate a uniformly frustrated 19-vertex model with an anisotropy parameter η by use of the density matrix renormalization group for the transfer matrix for 0.6⩽η⩽1.3. The scaling dimension x is calculated from eigenvalues of the transfer matrix for several values η. The finite-size scaling analyses with a logarithmic correction are carried out in order to determine transition temperatures. It is found that there are two kinds of phase transitions for 0.6≲η≲0.8, although there is a possibility of a single transition for 0.8≲η≲1.3. This result is not compatible with the result for the uniformly frustrated XY model.