Abstract
The Ising model on a one-dimensional monoatomic equidistant lattice with different nearest-neighbour and second-neighbour exchange interactions is researched. Generalized Kramers-Wannier transfer-matrix with translation on two periods of a lattice is introduced. A property similar to supercooling and superheating is detected. At the triple points phases are not individualized, but completely frustrated which corresponds to the phenomenon of critical opalescence. Exact analytical expressions for free energy, heat capacity and entropy including zero-temperature entropy are obtained. Various new special cases were analyzed and compared with all known results. All frustration fields for magnetization, frustration values for the zero-temperature entropy and magnetization are found.
Highlights
At the triple points phases are not individualized, but completely frustrated which corresponds to the phenomenon of critical opalescence
The first and most significant milestone in the theory of magnetism is Ernest Ising’s publication of his work in 1925 [1], in which he presented an exact analytical solution of the problem of the magnetic moments of atoms located at the sites of a one-dimensional lattice connected by a short-range exchange interaction and an external magnetic field
The Ising model, which long gone beyond the bounds of magnetism, has thousands and thousands of articles, reviews, monographs, conference proceedings, and their number is constantly growing
Summary
The first and most significant milestone in the theory of magnetism is Ernest Ising’s publication of his work in 1925 [1], in which he presented an exact analytical solution of the problem of the magnetic moments of atoms (spins) located at the sites of a one-dimensional lattice connected by a short-range exchange interaction and an external magnetic field. The Ising model on a one-dimensional monoatomic equidistant lattice with different nearest-neighbour and second-neighbour exchange interactions is researched. Generalized Kramers-Wannier transfer-matrix with translation on two periods of a lattice is introduced.
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