<p>In this work, we investigate the phase behavior of single-site adsorption models on one-dimensional (1D) lattice at nonzero temperatures, incorporating long-range intermolecular interactions up to the 12th neighbor. A comparative analysis of the models with different intermolecular potentials such as monotonic repulsive and attractive potentials with varying rates of decay, as well as a non-monotonic Lennard–Jones and oscillating potentials is performed. To accurately determine the thermodynamic properties of these systems, a tensor network approach to the well-known transfer matrix method is implemented. Characteristics of the models calculated in such way satisfy the conditions of thermodynamic equilibrium and belong to a formally infinite, truly thermodynamic, system. Using this approach, we have confirmed the remnants of “devil’s staircase” of phase transitions at nonzero temperatures in 1D system with repulsive interactions monotonically decreasing as <InlineEquation ID="IEq1"> <EquationSource Format="TEX">${r}^{-p}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>r</mi> </mrow> <mrow> <mo>-</mo> <mi>p</mi> </mrow> </msup> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$p=1, 2, 3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>. The cutoff radius of such interactions is shown to influence both the set of possible structures and their stability range. 1D systems with monotonically attractive, Lennard–Jones, and oscillating potentials demonstrate the first-order phase transition associated with condensation of lattice gas. In these cases, the type of intermolecular potential, the decay rate of the monotonic potential, and its cutoff radius do not qualitatively impact the phase behavior of the system. These results can be useful for an interpretation of experimental data in studies of adsorption in 1D adsorbents such as nanotubes and microporous solids.</p>

Long-Range Interactions in 1D Adsorption Models: Tensor Network Approach

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发表日期：

2026年1月17日

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Anastasiia V. Karpova,
Anastasiia I. Uliankina,
Vitaly A. Gorbunov,
Sergey S. Akimenko,
Alexander V. Myshlyavtsev

摘要

In this work, we investigate the phase behavior of single-site adsorption models on one-dimensional (1D) lattice at nonzero temperatures, incorporating long-range intermolecular interactions up to the 12th neighbor. A comparative analysis of the models with different intermolecular potentials such as monotonic repulsive and attractive potentials with varying rates of decay, as well as a non-monotonic Lennard–Jones and oscillating potentials is performed. To accurately determine the thermodynamic properties of these systems, a tensor network approach to the well-known transfer matrix method is implemented. Characteristics of the models calculated in such way satisfy the conditions of thermodynamic equilibrium and belong to a formally infinite, truly thermodynamic, system. Using this approach, we have confirmed the remnants of “devil’s staircase” of phase transitions at nonzero temperatures in 1D system with repulsive interactions monotonically decreasing as ${r}^{-p}$ $r^{- p}$ , where $p=1, 2, 3$ $p = 1, 2, 3$ . The cutoff radius of such interactions is shown to influence both the set of possible structures and their stability range. 1D systems with monotonically attractive, Lennard–Jones, and oscillating potentials demonstrate the first-order phase transition associated with condensation of lattice gas. In these cases, the type of intermolecular potential, the decay rate of the monotonic potential, and its cutoff radius do not qualitatively impact the phase behavior of the system. These results can be useful for an interpretation of experimental data in studies of adsorption in 1D adsorbents such as nanotubes and microporous solids.