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

Abstract

Ground-state and finite-temperature behaviour of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on decorated planar lattices consisting of inter-connected diamonds is investigated by means of the generalised decoration-iteration mapping transformation. The obtained exact results clearly point out that this model has a rather complex ground state composed of two unusual quantum phases, which is valid regardless of the lattice topology as well as the spatial dimensionality of the investigated system. It is shown that the diamond-like decorated planar lattices with a sufficiently high coordination number may exhibit a striking critical behaviour including reentrant phase transitions with two or three consecutive critical points.Copyright line will be provided by the publisher 1 Introduction Quantum Heisenberg models on geometrically frustrated planar lattices have enjoyed a great interest during the past decades especially due to their extraordinary diverse ground-state behaviour, which is often a result of mutual interplay between geometric frustration and quantum fluctuations [1,2,3]. From this perspective, geometrically frustrated quantum systems represent an excellent play ground for theoretical study of novel quantum many-body phenomena. Beside a rather complex ground state, which can be composed of several phases like the semi-classical Néel-like ordered phase, the quantum valence bond crystal phase or different disordered spin-liquid phases [1], quantum spin systems on two-dimensional geometrically frustrated lattices furnish a deeper insight into the quantum order-from-disorder effect [1,2,3], the scalar or vector chirality [4,5], as well as, the non-zero residual entropy that characterizes the macroscopic degeneracy of the ground state [1].

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

“…Note that both mapping parameters A and R are unambiguously determined by a self-consistency condition of the applied decoration-iteration mapping transformation and their explicit forms are given by equations (5)-(7) of reference [19]. At this stage, it is worthwhile to remark that the mapping relation (2.2) is universal and valid regardless of the lattice topology and spatial dimensionality of the model system.…”

“…Similarly, the sub-lattice and total magnetization can also be derived from the exact mapping equivalence (2.2) between the partition functions Z and Z Ising . More specifically, by combining equation (2.2) with the exact mapping theorems developed by Barry et al [28][29][30] and the generalized Callen-Suzuki spin identity [31][32][33], the sub-lattice magnetization m z i , m z h reduced per one Ising and Heisenberg spin, respectively, can be directly computed from the precise relations: [19] and the symbols . .…”

“…The hybrid Ising-Heisenberg models on diamond-like decorated lattices [11][12][13][14][15][16][17][18][19] belong to the simplest exactly solved quantum spin models, which were envisaged for describing lattice-statistical systems composed of the semi-classical Ising and the quantum Heisenberg spins. These simplified quantum-classical models can be rigorously treated within the framework of generalized decorationiteration mapping transformation [20][21][22], because the nodal Ising spins represent a barrier for quantum fluctuations that are consequently restricted to elementary diamond-shaped units only.…”

“…It is also worth mentioning that the Ising-Heisenberg models on the diamond-like decorated lattices have turned out to be a very useful testing ground for elucidating several typical quantum features. Indeed, these interesting but still exactly tractable spin systems may exhibit diverse quantum ordered and disordered ground states [11-15, 18, 19], the multi-step magnetization process with quantized intermediate magnetization plateaus [14,17,18], the enhanced magnetocaloric effect [14,18], as well as the non-trivial criticality [13,16,19].…”

“…In our recent works [11,16,19], we have examined in detail the ferromagnetic mixed spin-1/2 and spin-1 Ising-Heisenberg model on several diamond-like decorated planar lattices. It has been demonstrated that this hybrid classical-quantum model exhibits a rather rich ground-state and finite-temperature phase diagrams on account of the competition between the easy-axis Ising and the easy-plane Heisenberg interaction.…”