Transverse field effects on the competition between antiferromagnetic and cluster spin-glass phases

Effects of third-neighbor interactions on the frustrated quantum Ising model

We investigate thermal and quantum phase transitions of the J_{1}-J_{2}-J_{3} transverse Ising model on the square lattice. The model is studied within a cluster mean-field decoupling, which allows us to describe phase diagrams and the free-energy landscape in the neighborhood of phase transitions. Our findings indicate that the third-neighbor coupling (J_{3}) can affect the nature of phase transitions of the model. In particular, ferromagnetic third-neighbor couplings favor the onset of continuous order-disorder phase transitions, eliminating the tricritical point of the superantiferromagnetic-paramagnetic (SAFM-PM) phase boundary. On the other hand, the enhancement of frustration introduced by weak antiferromagnetic J_{3} gives rise to the staggered dimer phase favoring the onset of discontinuous classical phase transitions. Moreover, we find that quantum annealed criticality (QAC), which takes place when the classical discontinuous phase transition becomes critical by the enhancement of quantum fluctuations introduced by the transverse magnetic field, is eliminated from the SAFM-PM phase boundary by a relatively weak ferromagnetic J_{3}. Nevertheless, this change in the nature of phase transitions can still be observed in the presence of antiferromagnetic third-neighbor couplings being also found in the staggered-dimer phase boundary. Therefore, our findings support that QAC persists under the presence of frustrated antiferromagnetic third-neighbor couplings and is suppressed when these couplings are ferromagnetic, suggesting that frustration plays a central role in the onset of QAC.

Thermally driven state in a spin-1 model with competing interactions

We study a recently proposed spin-1 model with competing antiferromagnetic first-neighbor interaction and a third-neighbor coupling mediated by nonmagnetic states, which reproduces topological features of the phase diagrams of high-T_{c} superconductors [S. A. Cannas and D. A. Stariolo, Phys. Rev. E 99, 042137 (2019)2470-004510.1103/PhysRevE.99.042137]. We employ a cluster mean-field approach to investigate effects of crystal field anisotropy on the phase transitions hosted by this model. At low temperatures, the temperature-crystal field phase diagram exhibits superantiferromagnetic (SAF), antiferromagnetic (AF), and paramagnetic (PM) phases. In addition, we found a thermally driven state between SAF and PM phases. This thermally driven state and the SAF phase appears in the phase diagram as a domelike structure. Our calculations indicate that only second-order phase transitions occur in the PM-AF phase boundary, as suggested by previous Monte Carlo simulations.