The generalized density of states in a one-dimensional Ising model with ferrromagnetic and antiferromagnetic interactions
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866918248784592896 |
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| author | Kryzhanovsky, Boris Egorov, Vladislav |
| author_facet | Kryzhanovsky, Boris Egorov, Vladislav |
| contents | 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 $D_N(E,m)$, where $D_N(E,m)$ 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 $D(E)=\sum_m{D_N(E,m)}$. Nevertheless, the knowledge of quantity $D_N(E,m)$ 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 $\langle m(τ)\rangle$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12640 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The generalized density of states in a one-dimensional Ising model with ferrromagnetic and antiferromagnetic interactions Kryzhanovsky, Boris Egorov, Vladislav Disordered Systems and Neural Networks Statistical Mechanics 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 $D_N(E,m)$, where $D_N(E,m)$ 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 $D(E)=\sum_m{D_N(E,m)}$. Nevertheless, the knowledge of quantity $D_N(E,m)$ 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 $\langle m(τ)\rangle$. |
| title | The generalized density of states in a one-dimensional Ising model with ferrromagnetic and antiferromagnetic interactions |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2512.12640 |