We study the six-vertex model on the Sierpinski gasket, a four-coordinated hierarchical fractal with Hausdorff dimension $d_f=\log_23$. 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 $d_l=\log_2(5/2)\approx 1.3$. Finally, we propose a setup as an artificial spin ice to enable experimental study of the rich phenomenology of Sierpinski ice and its generalisations.
Fractal geometries provide a distinctive platform for controlling quantum interference, topology, and localization. We investigate the Su--Schrieffer--Heeger (SSH) model constructed on the Koch curve, where a triangular geometry enables additional same-sublattice hoppings that break chiral symmetry and modify the conve...
The reptation model postulates that entangled polymers slide within a fractal tube. Here we employ a model-independent relation between the zero-displacement probability and the mean-square displacement that applies to time-dependent fractal structures, enabling direct measurement of the fractal dimension $d_\mathrm{f}...
Xiaofei Tian, Qin-Han Liu, Zhi-Chao Yan et al.· 0 citations
We study two aspects of the abelian sandpile model on comb lattices. First, we prove that the infinite-volume limit of the stationary measures is supported on the saturated configuration. We then investigate the shape of avalanches induced by adding a particle at the origin in finite boxes of size $(2n+1)\times(2n+1)$...
Robin Kaiser, Ecaterina Sava-Huss, J. Überbacher· 1 citation· ⚡1
Using the two-dimensional Ashkin-Teller (AT) model, we compare criticality on three non-periodic lattices: the Smith-hat aperiodic tiling, Voronoi-Delaunay (VD) random triangulations, and uncorrelated diluted square lattices. The decay of the block-averaged coordination fluctuation $\sigma_Q$ with exponent $\alpha$ is...
We propose that, at criticality, equilibrium dynamics effectively evolves on a fractal subspace rather than throughout the full Euclidean space. Starting from Fisher's formulation of the order-parameter correlation function, we interpret the anomalous critical exponent $\eta$ geometrically through a correlation fractal...
We numerically study the bulk correlation functions in the two-dimensional Abelian sandpile model, aiming both to compare with the predictions of logarithmic conformal field theory and to extend the analysis to lattices where analytical methods are difficult to apply. Wilson's algorithm efficiently generates large-scal...
Qi-Yu Liu, Jan-Niklas Herre, Prajit Baruah et al.· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
