Fractional diffusion without disorder in two dimensions
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arXiv
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| Format: | Preprint |
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2025
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| author | Chakraborty, Nilotpal Heyl, Markus Moessner, Roderich |
| author_facet | Chakraborty, Nilotpal Heyl, Markus Moessner, Roderich |
| contents | We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale the path of a single defect exhibits anomalously long retractions, amounting to dynamical caging in a continuous-time random-walk framework, culminating in an effective fractional diffusion equation. Mapping to a height field yields an effective random walk subject to an emergent (entropic) logarithmic potential, whose strength is tunable, related to the exponent of algebraic ground-state correlations. The defect's path, viewed as non-equilibrium growth process, yields a frontier of fractal dimension of $5/4$, the value for a loop-erased random walk, rather than $4/3$ for simple and self-avoiding random walks. Such frustration/constraint-induced subdiffusion is expected to be relevant to platforms such as artificial spin ice and quantum simulators aiming to realize discrete link models and emergent gauge theories. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_00074 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional diffusion without disorder in two dimensions Chakraborty, Nilotpal Heyl, Markus Moessner, Roderich Mesoscale and Nanoscale Physics Disordered Systems and Neural Networks Statistical Mechanics We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale the path of a single defect exhibits anomalously long retractions, amounting to dynamical caging in a continuous-time random-walk framework, culminating in an effective fractional diffusion equation. Mapping to a height field yields an effective random walk subject to an emergent (entropic) logarithmic potential, whose strength is tunable, related to the exponent of algebraic ground-state correlations. The defect's path, viewed as non-equilibrium growth process, yields a frontier of fractal dimension of $5/4$, the value for a loop-erased random walk, rather than $4/3$ for simple and self-avoiding random walks. Such frustration/constraint-induced subdiffusion is expected to be relevant to platforms such as artificial spin ice and quantum simulators aiming to realize discrete link models and emergent gauge theories. |
| title | Fractional diffusion without disorder in two dimensions |
| topic | Mesoscale and Nanoscale Physics Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2504.00074 |