Equidistant versus bipartite ground states for 1D classical fluids at fixed particle density
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arXiv
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2025
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| author | Bétermin, Laurent Šamaj, Ladislav Travěnec, Igor |
| author_facet | Bétermin, Laurent Šamaj, Ladislav Travěnec, Igor |
| contents | We study the ground-state properties of one-dimensional fluids of classical (i.e., non-quantum) particles interacting pairwisely via a potential, at the fixed particle density $ρ$. Restricting ourselves to periodic configurations of particles, two possibilities are considered: an equidistant chain of particles with the uniform spacing $A=1/ρ$ and its simplest non-Bravais modulation, namely a bipartite lattice composed of two equidistant chains, shifted with respect to one another. Assuming the long range of the interaction potential, the equidistant chain dominates if $A$ is small enough, $0<A<A_c$. At a critical value of $A=A_c$, the system undergoes a continuous second-order phase transition from the equidistant chain to a bipartite lattice. The energy and the order parameter are singular functions of the deviation from the critical point $A-A_c$ with universal (i.e., independent of the model's parameters) mean-field values of critical exponents. The tricritical point at which the curve of continuous second-order transitions meets with the one of discontinuous first-order transitions is determined. The general theory is applied to the Lennard-Jones model with the $(n,m)$ Mie potential for which the phase diagram is constructed. The inclusion of a hard-core around each particle reveals a non-universal critical phenomenon with an $m$-dependent critical exponent. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_16639 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equidistant versus bipartite ground states for 1D classical fluids at fixed particle density Bétermin, Laurent Šamaj, Ladislav Travěnec, Igor Mathematical Physics 74G65, 74N05, 82B26 We study the ground-state properties of one-dimensional fluids of classical (i.e., non-quantum) particles interacting pairwisely via a potential, at the fixed particle density $ρ$. Restricting ourselves to periodic configurations of particles, two possibilities are considered: an equidistant chain of particles with the uniform spacing $A=1/ρ$ and its simplest non-Bravais modulation, namely a bipartite lattice composed of two equidistant chains, shifted with respect to one another. Assuming the long range of the interaction potential, the equidistant chain dominates if $A$ is small enough, $0<A<A_c$. At a critical value of $A=A_c$, the system undergoes a continuous second-order phase transition from the equidistant chain to a bipartite lattice. The energy and the order parameter are singular functions of the deviation from the critical point $A-A_c$ with universal (i.e., independent of the model's parameters) mean-field values of critical exponents. The tricritical point at which the curve of continuous second-order transitions meets with the one of discontinuous first-order transitions is determined. The general theory is applied to the Lennard-Jones model with the $(n,m)$ Mie potential for which the phase diagram is constructed. The inclusion of a hard-core around each particle reveals a non-universal critical phenomenon with an $m$-dependent critical exponent. |
| title | Equidistant versus bipartite ground states for 1D classical fluids at fixed particle density |
| topic | Mathematical Physics 74G65, 74N05, 82B26 |
| url | https://arxiv.org/abs/2502.16639 |