Dipole-Induced Transition in 3-Dimensions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911057958666240 |
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| author | Procaccia, Itamar Samanta, Tuhin |
| author_facet | Procaccia, Itamar Samanta, Tuhin |
| contents | The Kosterlitz-Thouless and the Hexatic phase transitions are celebrated examples of dipole (vortex, dislocation) induced transitions in condensed matter physics. For very clear reasons, these important ``topological" transitions are restricted to 2-dimensions. Here we present a genuine dipole-induced transition in the 3-dimensional response of (athermal) amorphous solids to applied strain. Similarly to the existence of a hexatic phase between normal solid and fluid, we identify an intermediate phase between a phase of normal elastic response at high pressure, and fluid matter at zero pressure. The mechanical response in the intermediate phase is accompanied by plasticity that is generically associated with ``non-affine" quadrupolar events seen in the resulting displacement field. Gradients of the quadrupolar fields act as dipole charges that screen elasticity, breaking both translational and Chiral symmetries. We highlight {\em angular} correlations that exhibit diverging correlation lengths at this transition and determine the critical scaling exponents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dipole-Induced Transition in 3-Dimensions Procaccia, Itamar Samanta, Tuhin Statistical Mechanics The Kosterlitz-Thouless and the Hexatic phase transitions are celebrated examples of dipole (vortex, dislocation) induced transitions in condensed matter physics. For very clear reasons, these important ``topological" transitions are restricted to 2-dimensions. Here we present a genuine dipole-induced transition in the 3-dimensional response of (athermal) amorphous solids to applied strain. Similarly to the existence of a hexatic phase between normal solid and fluid, we identify an intermediate phase between a phase of normal elastic response at high pressure, and fluid matter at zero pressure. The mechanical response in the intermediate phase is accompanied by plasticity that is generically associated with ``non-affine" quadrupolar events seen in the resulting displacement field. Gradients of the quadrupolar fields act as dipole charges that screen elasticity, breaking both translational and Chiral symmetries. We highlight {\em angular} correlations that exhibit diverging correlation lengths at this transition and determine the critical scaling exponents. |
| title | Dipole-Induced Transition in 3-Dimensions |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2507.11179 |