Quantum Potts Models on the Sierpiński Pyramid

Abstract

Phase transition of the two- and three-state quantum Potts models on the Sierpiński pyramid are studied by means of a tensor network framework, the higher-order tensor renormalization group method. Critical values of the transverse magnetic field and the magnetic exponent ${\hat{I}}^2$ are evaluated. Despite the fact that the Hausdorff dimension of the Sierpiński pyramid is exactly two $(={\log }_2^{}4)$, the obtained critical properties show that the effective dimension is lower than two.

4 pages, 3 figs