Ground-State Phase Diagram of Geometrically Frustrated Ising-Heisenberg Model on Doubly Decorated Planar Lattices

Abstract

Ground-state phase diagram of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on doubly decorated planar lattices is examined using the generalized decoration-iteration transformation. The main attention is devoted to the comparison of the ground-state properties of the quantum Ising-Heisenberg model and its semi-classical Ising analogue.PACS numbers: 05.50.+q, 75.10.Hk, 75.10.Jm Model system and its solutionConsider the mixed spin-1/2 and spin-1 Ising-Heisenberg model on doubly decorated planar lattices as schematically depicted on the left-hand

Reentrant phenomenon in the exactly solvable mixed spin-1/2 and spin-1 Ising-Heisenberg model on diamond-like decorated planar lattices

“…It is worth mentioning that all obtained results are universal as they hold regardless of whether ferromagnetic or antiferromagnetic interaction parameters J I and J H are assumed, as well as, independently of the lattice topology or spatial dimensionality of the investigated spin system. As proved, however, there are some fundamental differences between magnetic behaviour of models with distinct nature of the Heisenberg interaction (see our preliminary reports 32, 35, 36). Considering this fact, we will restrict ourselves here just to the case with the ferromagnetic Heisenberg interaction J H > 0.…”

“…Unfortunately, searching for the exact solution for the geometrically frustrated quantum Heisenberg models often fails due to a non‐commutability between spin operators involved in their Hamiltonians. Owing to this fact, we have recently proposed a special class of geometrically frustrated Ising–Heisenberg models on diamond‐like decorated lattices 32–38, which can be examined within the framework of an exact analytical approach based on the generalised decoration–iteration transformation 39–41. These simplified quantum models overcome the afore‐mentioned mathematical difficulty by introducing the Ising spins at nodal lattice sites and the Heisenberg dimers on interstitial decorating sites of the considered planar lattice.…”

“…It is worth mentioning that the mixed‐spin Ising–Heisenberg models with diamond‐like decorations turn out to be very useful testing ground for elucidating many quantum properties of low‐dimensional magnetic materials, in spite of the fact that the monomer–dimer interaction is considered as the Ising‐type interaction. Indeed, these rather simple spin models shed light on diverse quantum features to appear in the ground state 32–35, 38, the magnetisation process 34, 37, 38, the thermodynamics 34, 37, as well as, the critical behaviour 36. Note that kinetically frustrated diamond chain models constituted by nodal Ising spins and mobile electrons delocalised over the interstitial decorating sites have been particularly examined as well 42–44.…”

Phase transitions of geometrically frustrated mixed spin-1/2 and spin-1 Ising-Heisenberg model on diamond-like decorated planar lattices

“…In the former phase FRU 1 , the geometric frustration of the nodal Ising spins is caused by "non-magnetic" nature of the Heisenberg 13002-4 spin dimers |0, 0 , while the geometric frustration in the latter phase FRU 2 comes from antiferromagnetic spin states (either |1, −1 or | − 1, 1 ) of the Heisenberg spin pairs. As it has been shown in reference [15], both these phases can be regarded as special limiting cases of the unique frustrated phase FRU.…”

“…Now, let us proceed to the discussion of the finite-temperature behaviour of the antiferromagnetic spin-1/2 and spin-1 Ising-Heisenberg model on diamond-like decorated planar lattices. To enable a direct comparison with the ground-state analysis published in reference [15], we start first with the discussion of finite-temperature phase diagrams, which are displayed in figure 2 3) and, as a consequence, they represent the lines of the second-order phase transitions separating the spontaneously ordered phases (FRI 1 or FRI 3 ) from the disordered paramagnetic one. As one can clearly see from figure 2, the overall critical behaviour of the system very sensitively depends on the strength of the interaction parameters α and d, as well as, the topology (coordination number) of the lattice; for α < 1, the critical temperature t c either monotonously decreases upon decrease of the AZFS parameter until it tends towards zero temperature at the boundary value d = −1 (see the curves labeled as α = 0.1 and 0.5), or it exhibits an interesting non-monotonous dependence to be closely related to the FRI 1 → FRI 3 phase transition when the interaction ratio α is sufficiently close to the value α = 1 (see e.g.…”