Magnetic properties of the frustrated decorated Ising chain

TL;DR

This paper analyzes the magnetic properties of decorated Ising chains using exact transfer matrix methods, deriving thermodynamic characteristics, ground state entropy, and magnetization behaviors, revealing connections to Lucas and Pell numbers.

Contribution

It provides exact expressions for thermodynamic properties and ground state entropy of decorated Ising chains, linking ground state degeneracy to well-known numerical sequences.

Findings

Derived exact thermodynamic expressions for decorated Ising chains.

Identified ground state entropy related to Lucas and Pell numbers.

Calculated critical magnetic fields and magnetization plateaus.

Abstract

Using the Kramers-Wannier transfer matrix method we studied several decorated Ising chains. The exact expressions for thermodynamic characteristics, including the ground state characteristics, were obtained. We considered a number of modeling chains with different signs and absolute values of exchange constants for the nearest- and the next-nearest neighbors. For these models we calculated the magnetization curves. The critical values of magnetic fields and corresponding magnetization plateau parameters were obtained. Analytic expressions for the ground state entropy were obtained for the chains with different interaction constants. The dependencies of the number of states with minimum energy (the degeneration of the ground state) as the function of the number of particles were found. It was shown that these dependencies are expressed in terms of well-known numerical sequences - Lucas numbers and Pell numbers, which, in the limit of a large number of particles, are proportional to the powers of the golden and silver sections. Therefore, the ground state entropy (per particle) of the systems under consideration can be described in terms of these sections and, therefore, is nonzero.