Speaker
Description
The spin-$1/2$ Ising-Heisenberg model on the extended Lieb lattice in a magnetic field is solved using a combination of analytical and numerical methods. The decoration-iteration transformation [1] maps this model onto a spin-$1/2$ Ising model on the square lattice in an effective field, which can be solved exactly provided that the effective field becomes zero. Classical Monte Carlo simulations are then employed for the effective spin-$1/2$ Ising model on the square lattice, from which one may extract according to exact mapping correspondence rigorous numerical results for the spin-$1/2$ Ising-Heisenberg model on the extended Lieb lattice. The exact ground-state phase diagram reveals presence of quantum antiferromagnetic, monomer-dimer, ferrimagnetic, and ferromagnetic phases. In particular, we have explored the magnetization, magnetic susceptibility, entropy, and specific heat at finite temperatures. These quantities are particularly interesting close to a ground-state phase boundary between the monomer-dimer and ferrimagnetic phases, which extends to finite temperatures in the form of a line of discontinuous thermal phase transitions terminating at an Ising critical point. The anomalous response of basic magnetic and thermodynamic quantities can also be found for the quantum aftiferromagnetic phase, which contrarily exhibits at a given magnetic field a line of continuous thermal phase transitions.
Acknowledgements
This work was financially supported by The Ministry of Education, Research, Development and Youth of the Slovak Republic under the grant No. VEGA 1/0298/25, by the Slovak Research and Development Agency under Contract No. APVV-20-0150, and by the internal grant of Faculty of Science of Pavol Jozef Šafárik University in Košice under the contract No. VVGS-2025-3497.
References
[1] J. Strečka, “Generalized algebraic transformations and exactly solvable classical-quantum models,” Physics Letters A, vol. 374, no. 36. Elsevier BV, pp. 3718–3722, Aug. 2010. https://doi.org/10.1016/j.physleta.2010.07.030
