要旨 
This lecture reviews some recent achievements obtained in the field of exactly solvable latticestatistical spin models, which have been proposed to elucidate various cooperative phenomena in the condensed matter physics. Exact solution for several lowdimensional Ising and IsingHeisenberg models, which might be achieved by applying generalized mapping transformations, is discussed in connection with possible experimental realizations of those models. The special attention is devoted to possible macroscopic manifestations of lowdimensional quantum spin systems with a particular emphasis laid on the quantum entanglement of spin states, the quantum reduction of magnetization, the multistep magnetization plateaux, the enhanced magnetocaloric effect, the geometric frustration, etc.
Several planar IsingHeisenberg models [1] with a remarkable longrangeordering, which does not have any classical counterpart, will be discussed along with the trimerized and tetramerized IsingHeisenberg chains [2,3] exhibiting a multistep magnetization process with particular magnetization plateaux obeying quantized OshikawaYamanakaAffleck condition [4]. The frustrated IsingHeisenberg diamond chain [5] will be discussed in connection with an enhanced magnetocaloric effect as well as multistep magnetization process. The tetramerized ferroferroantiferroantiferro IsingHeisenberg bond alternating chain [3] will be investigated as a suitable model system for Cu(3Clpy)_{2}(N_{3})_{2} polymeric coordination compound. The ground state and thermodynamics of the frustrated spin1/2 Ising Heisenberg model on a triangular Kagome lattice, which exhibits extraordinary large residual entropy, will be examined in detail as an useful model system for a series of polymeric copper complexes Cu_{9}X_{2}(cpa)_{6}.xH_{2}O (X= F, Cl, Br, cpa=2carboxypentonic acid) [6].
Last but not least, the exact solution of several mixedspin Ising models on the decorated square [7], centered square [8], ShastrySutherland and bathroomtile [9] lattices will be investigated in view of rich critical behaviour they display. To the best of our knowledge, the mixedspin Ising model on the anisotropically decorated square lattice is the only longrangeordered spin system, which is quasi onedimensional in its nature [7]. On the other hand, the frustrated mixedspin Ising model on the centered square lattice exhibits very intriguing phase transition lines along which critical exponents vary continuously with interaction parameters and thus contradict the ordinary universality hypothesis [8].
The possible future extensions of generalized mapping transformation technique will be conjectured for the lowdimensional hybrid IsingHubbard and IsingHeisenberg models, while a spinphonon coupling possibly leading to a magnetoelastic spinPeierls phase transition might be possibly taken into account. Finally, the exact solution for the threedimensional models will be discussed in connection with a recent putative exact solution of the spin1/2 Ising model on the orthorhombic lattice [10].
[1] J. Strecka, M. Jascur, ; .
[2] J. Strecka, M. Jascur, .
[3] J. Strecka, M. Jascur, M. Hagiwara, K. Minami, Y. Narumi, K. Kindo, .
[4] M. Oshikawa, M. Yamanaka and I. Affleck, .
[5] L. Canova, J. Strecka, M. Jascur, .
[6] S. Maruti, L. W. ter Haar, S. Ateca, ; .
[7] J. Strecka, L. Canova, M. Jascur, .
[8] J. Strecka, , L. Canova, J. Dely, ; .
[9] J. Strecka, ; .
[10] Z.D. Zhang, .
