Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-09-16
Phys. Rev. E 84, 021125 (2011)
Physics
Condensed Matter
Statistical Mechanics
12 pages, 17 figures; Physical Review E (2011), in press
Scientific paper
10.1103/PhysRevE.84.021125
We investigate the symmetric Ashkin-Teller (AT) model on the triangular lattice in the antiferromagnetic two-spin coupling region ($J<0$). In the $J \rightarrow -\infty$ limit, we map the AT model onto a fully-packed loop-dimer model on the honeycomb lattice. On the basis of this exact transformation and the low-temperature expansion, we formulate a variant of worm-type algorithms for the AT model, which significantly suppress the critical slowing-down. We analyze the Monte Carlo data by finite-size scaling, and locate a line of critical points of the Ising universality class in the region $J<0$ and $K>0$, with K the four-spin interaction. Further, we find that, in the $J \rightarrow -\infty$ limit, the critical line terminates at the decoupled point $K=0$. From the numerical results and the exact mapping, we conjecture that this `tricritical' point ($J \rightarrow -\infty, K=0$) is Berezinsky-Kosterlitz-Thouless-like and the logarithmic correction is absent. The dynamic critical exponent of the worm algorithm is estimated as $z=0.28(1)$ near $(J \rightarrow -\infty, K=0)$.
Chen Qing-Hu
Deng Youjin
Lv Jian-Ping
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