Replicated liquid theory in $1+\infty$ dimensions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909900175572992 |
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| author | Tomita, Yukihiro Yoshino, Hajime |
| author_facet | Tomita, Yukihiro Yoshino, Hajime |
| contents | We develop a replicated liquid theory for structural glasses which exhibit spatial variation of physical quantities along one axis, say $z$-axis. The theory becomes exact with infinite transverse dimension $d-1 \to \infty$. It provides an exact free-energy functional with space-dependent glass order parameter $Δ_{ab}(z)$. As a first application of the scheme, we study diverging lengths associated with dynamic/static glass transitions of hardspheres with/without confining cavity. The exponents agree with those obtained in previous studies on related mean-field models. Moreover, it predicts a non-trivial spatial profile of the glass order parameter $Δ_{ab}(z)$ within the cavity which exhibits a scaling feature approaching the dynamical glass transition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21639 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Replicated liquid theory in $1+\infty$ dimensions Tomita, Yukihiro Yoshino, Hajime Soft Condensed Matter Disordered Systems and Neural Networks Statistical Mechanics We develop a replicated liquid theory for structural glasses which exhibit spatial variation of physical quantities along one axis, say $z$-axis. The theory becomes exact with infinite transverse dimension $d-1 \to \infty$. It provides an exact free-energy functional with space-dependent glass order parameter $Δ_{ab}(z)$. As a first application of the scheme, we study diverging lengths associated with dynamic/static glass transitions of hardspheres with/without confining cavity. The exponents agree with those obtained in previous studies on related mean-field models. Moreover, it predicts a non-trivial spatial profile of the glass order parameter $Δ_{ab}(z)$ within the cavity which exhibits a scaling feature approaching the dynamical glass transition. |
| title | Replicated liquid theory in $1+\infty$ dimensions |
| topic | Soft Condensed Matter Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2508.21639 |