Wavelets as a variational basis of the XY model

TL;DR

This paper introduces a wavelet-based variational approach to analyze the XY model in 2D and 3D, enabling the calculation of phase transition properties and low-temperature behavior.

Contribution

It applies Daubechies wavelets as a variational basis, providing a novel method to study phase transitions in the XY model.

Findings

Successfully describes the low-temperature phase.

Predicts the phase transition temperature.

Provides a framework for calculating observables.

Abstract

We use Daubechies' orthonormal compact wavelets as a variational basis for the $XY$ model in two and three dimensions. Assuming that the fluctuations of the wavelet coefficients are Gaussian and uncorrelated, minimization of the free energy yields the fluctuation strength of wavelet coefficients at different scales, from which observables can be computed. This model is able to describe the low-temperature phase and makes a prediction about the phase transition temperature.