On the Theory of Generalized Algebraic Transformations

Abstract

This book deals with the theory of generalized algebraic transformations, which is elaborated with the aim to provide a relatively simple theoretical tool that enables an exact treatment of diverse more complex lattice-statistical models. In addition to a brief historical account on the developments of this exact mapping method, the versatility of generalized algebraic transformations will be convincingly evidenced when providing exact results for two different families of exactly solvable models. The family of exactly solved Ising models brings a deeper insight into various 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.

72 pages, 9 figures, habilitation thesis defended at P. J. Safarik University in Kosice, Slovakia

Cited by in corpus (7)

• Direct algebraic mapping transformation for decorated spin models
• Effective low-energy description of almost Ising-Heisenberg diamond chain
• Unusual field-induced transitions in exactly solved mixed spin-(1/2,1) Ising chain with axial and rhombic zero-field splitting parameters
• Anomalous spin frustration enforced by a magnetoelastic coupling in the mixed-spin Ising model on decorated planar lattices
• Order-from-disorder effect in the exactly solved mixed spin-(1/2, 1) Ising model on fully frustrated triangles-in-triangles lattices
• Spin-phonon coupling induced frustration in the exactly solved spin-1/2 Ising model on a decorated planar lattice
• Exact solution and high temperature series expansion study of the 1/5-th depleted square lattice Ising model