Degeneracy of states in a one-dimensional spin chain

B. V. Kryzhanovsky, V. I. Egorov

Scientific Research Institute for System Analysis of the National Research Centre “Kurchatov Institute”, Moscow, Russian Federation

Abstract: We studied a one-dimensional spin model, one of the most detailed and thoroughly investigated exactly solvable models. Expressions for the density of states $D(E)$, representing the number of states with a given energy $E$, are well known. In this work, we derived expressions for the generalized density of states $D(E,m)$, which represent the number of states with a given energy $E$ and magnetization $m$. Knowing $D(E,m)$ allows us not only to calculate the system's thermodynamic properties but also to analyze the time evolution of spontaneous magnetization $m$. The expressions were derived for chains with both free and periodic boundary conditions.

Keywords: one-dimensional Ising model, the density of states, spontaneous magnetization, magnetization distribution.