Critical behavior of the 3-state Potts model on Sierpinski carpet

TL;DR

This study investigates the critical behavior of the 3-state Potts model on a Sierpinski carpet, revealing a second-order phase transition and providing bounds for critical exponents through finite-size scaling and Monte Carlo simulations.

Contribution

It is the first detailed analysis of the 3-state Potts model on a fractal lattice, demonstrating second-order transition characteristics and estimating critical exponents.

Findings

Phase transition is second order.

Critical exponents are estimated and consistent with hyperscaling.

Scaling corrections influence thermodynamic quantities.

Abstract

We study the critical behavior of the 3-state Potts model, where the spins are located at the centers of the occupied squares of the deterministic Sierpinski carpet. A finite-size scaling analysis is performed from Monte Carlo simulations, for a Hausdorff dimension $d_{f}$ $\simeq 1.8928$. The phase transition is shown to be a second order one. The maxima of the susceptibility of the order parameter follow a power law in a very reliable way, which enables us to calculate the ratio of the exponents $\gamma /\nu$. We find that the scaling corrections affect the behavior of most of the thermodynamical quantities. However, the sequence of intersection points extracted from the Binder's cumulant provides bounds for the critical temperature. We are able to give the bounds for the exponent $1/\nu$ as well as for the ratio of the exponents $\beta/\nu$, which are compatible with the results calculated from the hyperscaling relation.