Abstract. Ground-state and finite-temperature properties of the mixed spin-1 2 and spin-S Ising-Heisenberg diamond chains are examined within an exact analytical approach based on the generalized decoration-iteration map. A particular emphasis is laid on the investigation of the effect of geometric frustration, which is generated by the competition between Heisenberg-and Ising-type exchange interactions. It is found that an interplay between the geometric frustration and quantum effects gives rise to several quantum ground states with entangled spin states in addition to some semiclassically ordered ones. Among the most interesting results to emerge from our study one could mention a rigorous evidence for quantized plateux in magnetization curves, an appearance of the round minimum in the thermal dependence of susceptibility times temperature data, double-peak zero-field specific heat curves, or an enhanced magnetocaloric effect when the frustration comes into play. The triple-peak specific heat curve is also detected when applying small external field to the system driven by the frustration into the disordered state.PACS numbers: 05.50.+q, 75.10.Hk, 75.10.Jm, 75.10.Pq, 75.40.Cx Submitted to: J. Phys.: Condens. Matter IntroductionOver the last three decades, the low-dimensional quantum spin models with competing (frustrated) interactions have attracted considerable research interest especially due to their extraordinary diverse ground-state behaviour. Geometrically frustrated spin systems constitute a special sub-class of the frustrated models that can be distinguished by incapability of spins, inherent in their lattice positions, to simultaneously minimize the ground-state energy of each individual spin-spin interaction [1]. As a rule, the quantum spin systems affected by a rather strong geometric frustration often exhibit an exotic non-magnetic ground state (which does not have its classical analogue) in addition to a rich variety of the semi-classically ordered ones [2]. It is worthy to notice, moreover, ‡ Corresponding author: jozkos@pobox.sk [25], for which precise analytic solution is available leastwise for the ground state. Nevertheless, it should be pointed out that frustrated quantum systems are in general rather difficult to deal with, since extensive numerical methods must be used in order to obtain a reliable estimate of their magnetic properties. From this point of view, the one-dimensional (1D) frustrated spin systems are the simplest systems with respect to accurate treatment. Of these systems, the spin- [33]. Another remarkable finding relates to the observation of an inversion phenomenon, which can be induced in the frustrated diamond chain through the exchange anisotropy [34,35]. Note that the ground state and thermodynamics of the mixed-spin diamond chains containing also higher-spin sites have already been particularly examined as well [36]-[40].It is worthwhile to remark that 1D frustrated spin systems have initially been introduced purely as toy models suitable for investigating the ...

The geometric frustration of the spin-1/2 Ising-Heisenberg model on the triangulated Kagomé (triangles-in-triangles) lattice is investigated within the framework of an exact analytical method based on the generalized star-triangle mapping transformation. Ground-state and finite-temperature phase diagrams are obtained along with other exact results for the partition function, Helmholtz free energy, internal energy, entropy, and specific heat, by establishing a precise mapping relationship to the corresponding spin-1/2 Ising model on the Kagomé lattice. It is shown that the residual entropy of the disordered spin liquid phase is for the quantum Ising-Heisenberg model significantly lower than for its semi-classical Ising limit (S0/NTkB = 0.2806 and 0.4752, respectively), which implies that quantum fluctuations partially lift a macroscopic degeneracy of the ground-state manifold in the frustrated regime. The investigated model system has an obvious relevance to a series of polymeric coordination compounds Cu9X2(cpa)6 (X=F, Cl, Br and cpa=carboxypentonic acid) for which we made a theoretical prediction about the temperature dependence of zero-field specific heat.

Magnetization process of the mixed spin-1/2 and spin-3/2 Ising-Heisenberg diamond chain is examined by combining three exact analytical techniques: Kambe projection method, decoration-iteration transformation and transfer-matrix method. Multiple frustrationinduced plateaus in a magnetization process of this geometrically frustrated system are found provided that a relative ratio between the antiferromagnetic Heisenberg-and Ising-type interactions exceeds some particular value. By contrast, there is just a single magnetization plateau if the frustrating Heisenberg interaction is sufficiently small compared to the Ising one.

The generalized decoration-iteration transformation is adopted to treat exactly a hybrid model of doubly decorated two-dimensional lattices, which have localized Ising spins at their nodal lattice sites and itinerant electrons delocalized over pairs of decorating sites. Under the assumption of a half filling of each couple of the decorating sites, the investigated model system exhibits a remarkable spontaneous antiferromagnetic longrange order with an obvious quantum reduction in the staggered magnetization. It is shown that the critical temperature of the spontaneously long-range ordered quantum antiferromagnet displays an outstanding nonmonotonic dependence on a ratio between the kinetic term and the Ising-type exchange interaction.

Magnetic properties of a diamond chain consisting of spin-1/2 Ising-and Heisenbergtype atoms are investigated using the generalized decoration-iteration technique that removes all the Heisenberg-type atoms from the diamond chain and substitutes these atoms by new effective couplings. Exact results for the magnetization, enthalpy, Gibbs free energy, specific heat, entropy and susceptibility are obtained for zero and nonzero external magnetic field. Numerical results for the ground-state phase diagram are investigated in detail.

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

The mixed spin-1/2 and spin-1 Ising-Heisenberg ferromagnet on the decorated triangular lattice consisting of inter-connected diamonds is investigated within the framework of an exact decoration-iteration mapping transformation. It is shown that the diamond-like decoration by a couple of the Heisenberg spins gives rise to a diverse critical behaviour including reentrant phase transitions with two consecutive critical points.

The mixed spin-(1/2, SB, SC) Ising model on a decorated square lattice with two different kinds of decorating spins SB and SC (SB = SC) placed on its horizontal and vertical bonds, respectively, is exactly solved by establishing a precise mapping relationship with the corresponding spin-1/2 Ising model on an anisotropic square (rectangular) lattice. The effect of uniaxial single-ion anisotropy acting on both types of decorating spins SB and SC is examined in particular. If decorating spins SB and SC are integer and half-odd-integer, respectively, or if the reverse is the case, the model under investigation displays a very peculiar critical behavior beared on the spontaneously ordered 'quasi-1D' spin system, which appears as a result of the single-ion anisotropy strengthening. We have found convincing evidence that this remarkable spontaneous ordering virtually arises even though all integer-valued decorating spins tend towards their 'non-magnetic' spin state S = 0 and the system becomes disordered only upon further increase of the single-ion anisotropy. The single-ion anisotropy parameter is also at an origin of various temperature dependences of the total magnetization when imposing the pure ferrimagnetic or the mixed ferro-ferrimagnetic character of the spin arrangement.