Universal critical properties of the Eulerian bond-cubic model |
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| Authors: | Ding Cheng-Xiang Yao Gui-Yuan Li Song Deng You-Jin and Guo Wen-An |
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| Institution: | Physics Department, Beijing Normal University, Beijing 100875, China;Physics Department, Beijing Normal University, Beijing 100875, China;Analysis and Testing Center, Beijing Normal University, Beijing 100875, China;Hefei National Laboratory for Physical Sciences at Microscale, Department of Modern Physics, University of Science and Technology of China, Hefei 230027, China;Physics Department, Beijing Normal University, Beijing 100875, China |
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| Abstract: | 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. |
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| Keywords: | phase transition and critical phenomena Eulerian-bond cubic model Monte Carlo simulation fractal dimension |
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