We investigate the thermodynamic properties of the frustrated bilayer quantum Heisenberg antiferromagnet at low temperatures in the vicinity of the saturation magnetic field. The low-energy degrees of freedom of the spin model are mapped onto a hard-square gas on a square lattice. We use exact diagonalization data for finite spin systems to check the validity of such a description. Using a classical Monte Carlo method we give a quantitative description of the thermodynamics of the spin model at low temperatures around the saturation field. The main peculiarity of the considered two-dimensional Heisenberg antiferromagnet is related to a phase transition of the hard-square model on the square lattice, which belongs to the two-dimensional Ising model universality class. It manifests itself in a logarithmic (low-) temperature singularity of the specific heat of the spin system observed for magnetic fields just below the saturation field.
In this paper, we performed the comprehensive studies of magnetic frustration properties in the Ising model on a decorated square lattice in the framework of an exact analytical approach based on the Kramers-Wannier transfer matrix method. The assigned challenge consisted in finding rigorous formulas for residual entropies of all possible cases of degeneration of the system without exception and also elucidating the influence of frustrations on the behavior of the thermodynamic functions of the system under discussion. The accomplished results turned out to be very rich and intricate, especially in comparison with the original undecorated square lattice, in which frustration properties are completely absent. Such an abundance of properties is due to the multiparametric problem of decorated lattice with four exchange interactions J_{x}, J_{y}, J_{dx}, and J_{dy} taking on arbitrary continuous values and different signs: positive (ferromagnetic) and negative (antiferromagnetic), as well as with two discrete variables d_{x} and d_{y} (multiplicities of decorating spins in both lattice directions), corresponding to infinite natural series of numbers.
Abstract We study the temperature dependence of the thermodynamic properties of spin-1/2 antiferromagnets on two-dimensional lattices. Our analysis employs the sine-square deformation (SSD), in which a real-space envelope function is applied to the Hamiltonian so that the local energy scale is smoothly reduced to zero at the system boundaries. The quantum eigenstates of the SSD Hamiltonian exhibit bulk-like behavior near the system center, effectively mimicking the thermodynamic limit even in small finite-size calculations. Using these fictitious bulk states, we compute the energy density, specific heat, and magnetic susceptibility as functions of temperature. We find that both the triangular- and kagome-lattice antiferromagnets show either a shoulder or a pronounced double-peak structure in the low-temperature specific heat, whereas the kagome case particularly shows a strong enhancement of magnetic susceptibility down to the lowest temperature range. These direct comparisons, together with the square-lattice and one-dimensional cases, reveal that although both frustrated systems retain a substantial amount of entropy, the low-energy excitations below ∼ 0.5 J
∼0.5J of the kagome lattice are predominantly governed by the magnetic excited states, whereas not much for the triangular lattice.