Universal critical properties of the Eulerian bond-cubic model

doi:10.1088/1674-1056/20/7/070504

中国物理B ›› 2011, Vol. 20 ›› Issue (7): 70504-070504.doi: 10.1088/1674-1056/20/7/070504

Universal critical properties of the Eulerian bond-cubic model

李崧¹, 邓友金², 丁成祥³, 姚桂元³, 郭文安³

(1)Analysis and Testing Center, Beijing Normal University, Beijing 100875, China; (2)Hefei National Laboratory for Physical Sciences at Microscale, Department of Modern Physics, University of Science and Technology of China, Hefei 230027, China; (3)Physics Department, Beijing Normal University, Beijing 100875, China

收稿日期:2011-03-25 修回日期:2011-04-01 出版日期:2011-07-15 发布日期:2011-07-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10675021), the New Century Excellent Talents in University of China, the Natural Science Foundation of Anhui Province of China (Grant No. 090416224), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20103402110053).

Universal critical properties of the Eulerian bond-cubic model

Ding Cheng-Xiang(丁成祥)^a), Yao Gui-Yuan(姚桂元)^a), Li Song(李崧)^b)†, Deng You-Jin(邓友金)^c)‡, and Guo Wen-An(郭文安)^a)

^a Physics Department, Beijing Normal University, Beijing 100875, China; ^b Analysis and Testing Center, Beijing Normal University, Beijing 100875, China; ^c Hefei National Laboratory for Physical Sciences at Microscale, Department of Modern Physics, University of Science and Technology of China, Hefei 230027, China

Received:2011-03-25 Revised:2011-04-01 Online:2011-07-15 Published:2011-07-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10675021), the New Century Excellent Talents in University of China, the Natural Science Foundation of Anhui Province of China (Grant No. 090416224), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20103402110053).

摘要/Abstract

摘要： 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.

关键词: phase transition and critical phenomena, Eulerian-bond cubic model, Monte Carlo simulation, fractal dimension

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.

Key words: phase transition and critical phenomena, Eulerian-bond cubic model, Monte Carlo simulation, fractal dimension

中图分类号: (Lattice theory and statistics)

05.50.+q

64.60.Cn (Order-disorder transformations) 64.60.F- (Equilibrium properties near critical points, critical exponents) 75.10.Hk (Classical spin models)

丁成祥, 姚桂元, 李崧, 邓友金, 郭文安. Universal critical properties of the Eulerian bond-cubic model[J]. 中国物理B, 2011, 20(7): 70504-070504.

Ding Cheng-Xiang(丁成祥), Yao Gui-Yuan(姚桂元), Li Song(李崧), Deng You-Jin(邓友金), and Guo Wen-An(郭文安) . Universal critical properties of the Eulerian bond-cubic model[J]. Chin. Phys. B, 2011, 20(7): 70504-070504.

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Universal critical properties of the Eulerian bond-cubic model

Universal critical properties of the Eulerian bond-cubic model

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