Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-09-26
Chinese Physics B, 20, 070504 (2011)
Physics
Condensed Matter
Statistical Mechanics
Scientific paper
We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical exponents of the model are determined for several values of $n$. Two of the exponents are fractal dimensions, which are obtained numerically for the first time. Our results are consistent with the Coulomb gas predictions for the critical O($n$) branch for $n < 2$ and the results obtained by previous transfer matrix calculations. For $n=2$, we find that the thermal exponent, the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical O(2) loop model. These results confirm that the cubic anisotropy is marginal at $n=2$ but irrelevant for $n<2$.
Deng Youjin
Ding Cheng-Xiang
Guo Wen-An
Li Song
Yao Gui-Yuan
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