Partition function zero calculation of q-state clock model using higher-order tensor renormalization group

Abstract

We investigate the partition function zeros of 2D q-state clock model on the square lattice by using higher- order tensor renormalization group (HOTRG) method. We use the higher-order singular value decomposition (HOSVD) to truncate the bond dimension of contracted tensor up to D=50. For q=5, 6, 8, and 10, we perform the finite size scaling of the leading zero up to the system size 128 x 128. We find that the scaling behavior of the leading zeros for q>=6 at the high-temperature transition region is of the BKT form including the XY-limit, while the behavior for 5-state clock model differs from the larger q's.