Exact solution and pair correlation functions for a generalized three-chain Ising tube with multispin interactions
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| Format: | Preprint |
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2026
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| author | Khrapov, Pavel Volkov, Nikita |
| author_facet | Khrapov, Pavel Volkov, Nikita |
| contents | We obtain an exact solution for a generalized three-chain Ising tube (TCGIT) of length $L$ with toroidal boundary conditions and the most general $C_3$-invariant Hamiltonian on an elementary prism, containing 20 independent coupling constants, including an external magnetic field. Using an $8\times 8$ transfer matrix, we derive the exact partition function of the finite system and obtain the free energy, internal energy, specific heat, magnetization, magnetic susceptibility, and entropy in the thermodynamic limit $L\to\infty$. In the general case, $λ_{\max}$ is determined by a quartic equation, whereas in the principal special case with even-spin interactions (PSC) the spectrum simplifies substantially: the characteristic polynomial factorizes, and $λ_{\max}$ is given by the root of a quadratic equation. For mirror-symmetric subfamilies, we derive explicit formulas for the pair correlation functions and express the magnetization in terms of the components of the eigenvector associated with $λ_{\max}$; in the even-spin case with $h=0$, the magnetization vanishes. Important special cases include the width-three planar model with nearest-neighbor, next-nearest-neighbor, and plaquette interactions, including the entropy limit $S(T\to0^+)=(\ln 2)/3$ for $k\ge 0$ and $S(T\to0^+)=0$ for $k<0$, as well as the width-three planar triangular model with distinct nearest-neighbor couplings, three-spin interactions involving neighboring triangles, and an external field. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_17600 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact solution and pair correlation functions for a generalized three-chain Ising tube with multispin interactions Khrapov, Pavel Volkov, Nikita Statistical Mechanics 82B20, 82B23 We obtain an exact solution for a generalized three-chain Ising tube (TCGIT) of length $L$ with toroidal boundary conditions and the most general $C_3$-invariant Hamiltonian on an elementary prism, containing 20 independent coupling constants, including an external magnetic field. Using an $8\times 8$ transfer matrix, we derive the exact partition function of the finite system and obtain the free energy, internal energy, specific heat, magnetization, magnetic susceptibility, and entropy in the thermodynamic limit $L\to\infty$. In the general case, $λ_{\max}$ is determined by a quartic equation, whereas in the principal special case with even-spin interactions (PSC) the spectrum simplifies substantially: the characteristic polynomial factorizes, and $λ_{\max}$ is given by the root of a quadratic equation. For mirror-symmetric subfamilies, we derive explicit formulas for the pair correlation functions and express the magnetization in terms of the components of the eigenvector associated with $λ_{\max}$; in the even-spin case with $h=0$, the magnetization vanishes. Important special cases include the width-three planar model with nearest-neighbor, next-nearest-neighbor, and plaquette interactions, including the entropy limit $S(T\to0^+)=(\ln 2)/3$ for $k\ge 0$ and $S(T\to0^+)=0$ for $k<0$, as well as the width-three planar triangular model with distinct nearest-neighbor couplings, three-spin interactions involving neighboring triangles, and an external field. |
| title | Exact solution and pair correlation functions for a generalized three-chain Ising tube with multispin interactions |
| topic | Statistical Mechanics 82B20, 82B23 |
| url | https://arxiv.org/abs/2605.17600 |