Monte Carlo study of the XY-model on Sierpinski gasket

TL;DR

This study uses Monte Carlo simulations to investigate the XY-model on Sierpinski gaskets, finding no finite-temperature phase transition, aligning with previous harmonic approximation results and similar to Ising models on fractals.

Contribution

It provides the first Monte Carlo analysis of the XY-model on Sierpinski gaskets, confirming the absence of phase transition at finite temperatures.

Findings

No finite-temperature phase transition detected

Results agree with harmonic approximation studies

Consistent with Ising model behavior on fractals

Abstract

We have performed a Monte Carlo study of the classical XY-model on two-dimensional Sierpinski gaskets of several cluster sizes. From the dependence of the helicity modulus on the cluster size we conclude that there is no phase transition in this system at a finite temperature. This is in agreement with previous findings for the harmonic approximation to the XY-model on Sierpinski gasket and is analogous to the absence of finite temperature phase transition for the Ising model on fractals with a finite order of ramification.