We study the effects of a transverse magnetic field on the $J_1\text{−}{J}_2\text{−}{J}_3$ Ising model on the honeycomb lattice. By employing the cluster mean-field method, we investigate the nature of classical and quantum phase transitions, entropy accumulation, and the Grüneisen parameter focusing in the case with ferromagnetic first-neighbor interactions ($J_1>0$) and antiferromagnetic third-neigbor interactions ($J_3<0$). This frustrated model exhibits a competition between the zigzag (ZZ) antiferromagnetic and ferromagnetic (FE) phases that can be controlled by tuning $g_2=J_2/J_1$. Our findings indicate only continuous phase transitions between FE and paramagnetic (PM) phases in both classical and quantum limits. On the other hand, the ZZ-PM phase boundary can exhibit both classical and quantum tricriticality, with first-order phase transitions appearing near the regime of strong competition between FE and ZZ phases. We also find that increasing the transverse magnetic field can transform classical first-order transitions into continuous phase transitions across the ZZ-PM phase boundary, introducing a tricritical point in the field-temperature phase diagram. We map a wide range of competing interactions over which this phenomenon, called quantum annealed criticality, emerges through the interplay of classical and quantum fluctuations. Furthermore, entropy accumulation and a pronounced inverse magnetocaloric effect occur close to the quantum critical point and are particularly enhanced in scenarios where quantum annealed criticality is present. The relevance of our results to magnetic van der Waals materials exhibiting Ising anisotropy is also discussed.

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• Magnetic phase transitions
• Magnetocaloric effect
• Quantum criticality
• Quantum phase transitions
• 2-dimensional systems
• Exact diagonalization
• Mean-field & cluster methods