Phase diagram and critical behaviour of disordered quantum clock model

We investigate the critical behaviour of the phase transitions in the disordered quantum clock model using large-scale Monte Carlo simulations. We recast the model via the quantum-to-classical mapping onto a higher-dimensional classical spin Hamiltonian with the columnar disorder. The quasi-long-range ordered (QLRO) phase that separates the clock-ordered phase and paramagnetic phase survives at weak disorder but shrinks as the strength of the disorder increases. The QLRO phase vanishes at a tricritical point, beyond which there is a direct transition from the clock-ordered phase to the paramagnetic phase. The transition from the QLRO phase to the paramagnetic phase displays a crossover from clean-XY critical behaviour to disorder-dependent critical behaviour, similar to the behaviour observed in the (1+1) d disordered XY model [1]. However, the critical behaviour of the transition from the clock-ordered phase to the QLRO phase appears to be independent of the disorder strength. The direct transition between the clock-ordered and paramagnetic phases above the tricritical point also shows a disorder-dependent critical behaviour. At very high disorder strengths, we see signatures of the infinite randomness fixed-point as predicted by the strong disorder renormalization group calculations [2].

[1]. F. Hrahsheh and T. Vojta, Phys. Rev. Lett.109, 265303 (2012).

[2]. T. Senthil and S. N. Majumdar, Phys. Rev. Lett.76, 3001 (1996).