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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2602.24051 |
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| _version_ | 1866911473816567808 |
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| author | Canals, Benjamin |
| author_facet | Canals, Benjamin |
| contents | The emergence of order and geometric limit shapes in a three-dimensional (3D) Coulomb phase subject to domain wall boundary conditions (DWBC) is investigated. While the arctic circle phenomenon -- the spatial segregation of frozen and fluctuating degrees of freedom -- is well-established in the two-dimensional six-vertex model (square ice), its extension to 3D remains largely unexplored. A cubic lattice model with Ising degrees of freedom living on the edges, whose ground state manifold is governed by a divergence-free (3-in/3-out) local constraint, is considered. In the bulk, this model realizes a classical spin liquid characterized by algebraic correlations and pinch-point singularities in reciprocal space. It is demonstrated that applying DWBC partially lifts the extensive ground state degeneracy, inducing long-range magnetic order in the thermodynamic limit. Despite this ordering, it is found that the system retains a fluctuating component that exhibits the signature of a Coulomb phase. Finally, by mapping the local vertex polarization density, compelling numerical support is provided for a 3D generalization of the arctic limit shape, bridging the gap between topological constraints and emergent geometry in higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_24051 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Emergence of geometric order from topological constraints in a three-dimensional Coulomb phase Canals, Benjamin Strongly Correlated Electrons Statistical Mechanics The emergence of order and geometric limit shapes in a three-dimensional (3D) Coulomb phase subject to domain wall boundary conditions (DWBC) is investigated. While the arctic circle phenomenon -- the spatial segregation of frozen and fluctuating degrees of freedom -- is well-established in the two-dimensional six-vertex model (square ice), its extension to 3D remains largely unexplored. A cubic lattice model with Ising degrees of freedom living on the edges, whose ground state manifold is governed by a divergence-free (3-in/3-out) local constraint, is considered. In the bulk, this model realizes a classical spin liquid characterized by algebraic correlations and pinch-point singularities in reciprocal space. It is demonstrated that applying DWBC partially lifts the extensive ground state degeneracy, inducing long-range magnetic order in the thermodynamic limit. Despite this ordering, it is found that the system retains a fluctuating component that exhibits the signature of a Coulomb phase. Finally, by mapping the local vertex polarization density, compelling numerical support is provided for a 3D generalization of the arctic limit shape, bridging the gap between topological constraints and emergent geometry in higher dimensions. |
| title | Emergence of geometric order from topological constraints in a three-dimensional Coulomb phase |
| topic | Strongly Correlated Electrons Statistical Mechanics |
| url | https://arxiv.org/abs/2602.24051 |