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

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

2003-03-10

arxiv.org/abs/cond-mat/0303175v1

Phys. Rev. B 65 (2002) 184427

Physics

Condensed Matter

Statistical Mechanics

13 pages, 4 figures

Scientific paper

10.1103/PhysRevB.65.184427

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.

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