DMRG study of the Berezinskii-Kosterlitz-Thouless transitions of the 2D 5-state clock model

Christophe Chatelain (1)

1 IJL - Institut Jean Lamour

The two Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional 5-state clock model are studied on infinite strips using the DMRG algorithm. Because of the open boundary conditions, the helicity modulus $\Upsilon_2$ is computed by imposing twisted magnetic fields at the two boundaries. Its scaling behavior is in good agreement with the existence of essential singularities with $\sigma=1/2$ at the two transitions. The predicted universal values of $\Upsilon_2$ are shown to be reached in the thermodynamic limit. The fourth-order helicity modulus is observed to display a dip at the low-temperature BKT transition, like the XY model. Finally, the scaling behavior of magnetization at the low temperature transition is compatible with $\eta=1/4$.

Mots clés: clock model; DMRG algorithm; Berezinskii-Kosterlitz-Thouless transition

Domaines: Mécanique statistique [cond-mat.stat-mech]

Christophe Chatelain. DMRG study of the Berezinskii-Kosterlitz-Thouless transitions of the 2D 5-state clock model. 2014. ⟨hal-01035449v1⟩