Universal critical properties of the Eulerian bond-cubic model

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

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.

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

Received: 25 March 2011
Revised: 01 April 2011
Accepted manuscript online:

PACS:	05.50.+q	(Lattice theory and statistics)
	64.60.Cn	(Order-disorder transformations)
	64.60.F-	(Equilibrium properties near critical points, critical exponents)
	75.10.Hk	(Classical spin models)

Fund: 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).

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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 2011 Chin. Phys. B 20 070504

[1]	Blöte H W J and Nightingale M P 1984 Physica A 129 1
[2]	Guo W A, Qian X F and Blöte H W J 2006 Phys. Rev. E 73 026104
[3]	Potts R B 1954 Proc. Camb. Phil. Soc. 48 106
[4]	Wu F Y 1982 Rev. Mod. Phys. 54 235
[5]	Kasteleyn P W and Fortuin C M 1969 J. Phys. Soc. Japan 46 (suppl.) 11
[6]	Fortuin C M and Kasteleyn P W 1972 Physica 57 536
[7]	Stanley H W 1974 Phase Transitions and Critical Phenomena Vol. 3 (London: Academic Press)
[8]	Chayes L and Machta J 1997 Physica A 239 542
[9]	Chayes L and Machta J 1998 Physica A 254 477
[10]	Swendsen R H and Wang J S 1987 Phys. Rev. Lett. 58 86
[11]	Ding C X, Deng Y, Guo W A, Qian X F and Blöte H W J 2007 J. Phys. A: Math. Theor. 40 3305
[12]	Deng Y, Garoni T M, Guo W A, Blöte H W J and Sokal A D 2007 Phys. Rev. Lett. 98 120601
[13]	Qian X F, Deng Y and Blöte H W J 2005 Phys. Rev. E 71 016709
[14]	Ding C X, Deng Y, Guo W A and Blöte H W J 2009 Phys. Rev. E 79 061118
[15]	Wolff U 1989 Phys. Rev. Lett. 62 361
[16]	Stauffer D and Aharony A 1984 Introduction to Percolation Theory 2nd edn. (London: Taylor & Francis)
[17]	Nightingale M P 1990 Finite-Size Scaling and Numerical Simulation of Statistical Systems (Singapore: World Scientific)
[18]	Barber M N 1983 Phase Transitions and Critical Phenomena Vol. 8 (New York: Academic Press)
[19]	Nienhuis B 1982 Phys. Rev. Lett. 49 1062
[20]	Nienhuis B 1984 J. Stat. Phys. 34 731
[21]	Saleur H and Duplantier B 1987 Phys. Rev. Lett. 58 2325
[22]	Duplantier B 2000 Phys. Rev. Lett. 84 1363
[23]	den Nijs M P M 1981 Phys. Rev. B 23 6111
[24]	Knops H J F 1980 Ann. Phys. 128 448
[25]	Baxter R J 1982 Exactly Solved Models in Statistical Mechanics (London: Academic Press)

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