Multifractal analysis of the symmetry of a strictly isospectral energy landscape on a square lattice

We use the Hoder regularity analysis to study the symmetry breaking and recovery due to a parametric potential generated via the strictly isospectral factorization method. The initial potential is twodimensional and periodic in the two Cartesian directions, with the symmetry group P-4mm. The resulting parametric isospectral potential display a P-m symmetry for values of the parameter moderately close to the singular value gamma(s). However, at large values of the parameter, visually around gamma = gamma(s) + 110, the original symmetry is recovered. For a much higher precision value of the parameter for this symmetry recovery, we show that the multifractal spectrum of the parametric potential can be conveniently used. In the latter case, we obtain gamma = gamma(s) + 201:085 for three decimal digits precision. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

In this study, we investigated symmetry breaking and recovery induced by a parametric potential generated via the strictly isospectral factorization method using Hoder regularity analysis. The parametric isospectral potential displayed a P-m symmetry for values moderately close to the singular value, but the original symmetry was recovered at large parameter values. A multifractal spectrum analysis revealed a convenient method for detecting symmetry recovery at a much higher precision value of the parameter.