Fractal deconfinement and confinement in Sierpinski ice

2026/08/03 by James Walkling, Roderich Moessner
Physics and Astronomy · #cond-mat.stat-mech

paper · pdf

8+10 pages, 5+8 figures

arxiv created 2026/08/03 · arxiv updated 2026/08/05

Abstract

We study the six-vertex model on the Sierpinski gasket, a four-coordinated hierarchical fractal with Hausdorff dimension d_f=log₂3. Given the importance of dimensionality for the long-wavelength behavior of such models, we specifically consider correlations and confinement as a function of the vertex weights, with the equal-weight point corresponding to the ice model. We calculate the partition function and correlators recursively to obtain a rich phase diagram hosting many different regimes. While the ice model shows entropic charge confinement, a particular four-vertex limit exhibits fractal deconfinement, with the string joining the deconfined charges itself a statistical fractal with fractal dimension d_l=log₂(5/2)≈ 1.3. Finally, we propose a setup as an artificial spin ice to enable experimental study of the rich phenomenology of Sierpinski ice and its generalisations.

Citations

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