Monte Carlo study of the XY-model on Sierpnski carpet

TL;DR

This study uses Monte Carlo simulations with the Wolff cluster algorithm to investigate the XY-model on a Sierpiński carpet, revealing no finite-temperature BKT transition due to the fractal structure's properties.

Contribution

First Monte Carlo analysis of the XY-model on a Sierpiński carpet demonstrating the absence of BKT transition in this fractal system.

Findings

No finite-temperature BKT transition observed

Susceptibility and helicity modulus results support the absence of transition

Fractal structure influences phase transition behavior

Abstract

We have performed a Monte Carlo study of the classical XY-model on a Sierpi\' nski carpet, which is a planar fractal structure with infinite order of ramification and fractal dimension 1.8928. We employed the Wolff cluster algorithm in our simulations and our results, in particular those for the susceptibility and the helicity modulus, indicate the absence of finite-temperature Berezinskii-Kosterlitz-Thouless (BKT) transition in this system.