On the Theory of Generalized Algebraic Transformations : Algebraic Mapping Transformations and Exactly Solvable Models in Statistical Mechanics

The present book deals with the theory of generalized algebraic transformations, which is elaborated with the aim to provide a relatively simple mapping method that enables an exact treatment of various more complex lattice-statistical models. The versatility of this rigorous mapping technique has been convincingly evidenced in two different families of exactly solvable models. The family of exactly solved Ising models brought a deeper insight into diverse aspects closely associated especially with phase transitions and critical phenomena. The second class of exactly solved Ising-Heisenberg models sheds light on striking quantum manifestations of spontaneously long-range ordered systems, which are closely connected with a mutual interplay between quantum and cooperative phenomena.