2025/12/14 by Boris Kryzhanovsky, Kryzhanovsky, Boris, V. I. Egorov +1
Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Opinion Dynamics and Social Influence #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2512.12640
openalex publication_date 2025/12/14 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28
Expressions for the density of states D(E), where D(E) is the number of states of energy E, are well known. The present paper offers the expressions for generalized density of states DN(E,m), where DN(E,m) is the number of states with energy E and magnetization m in a one-dimensional N-spin chain. The expressions obtained here can be considered as reference ones, since all the main characteristics were obtained without them: using the transfer matrix technique or using well-known expressions for the density of states D(E)=∑mDN(E,m). Nevertheless, the knowledge of quantity DN(E,m) helps to understand the model properties and allows the analysis of the temporal behavior of magnetization m=m(τ). In particular, we demonstrate that in a one-dimensional model spontaneous magnetization can be observed at a non-zero temperature. However, the spontaneous magnetization can randomly change its sign, which results in the magnetization averaged over a very long observation period becoming zero ⟨ m(τ)⟩.