Two-Point Resistance on the Centered-Triangular Lattice
M. Q. Owaidat1,2** , A. A. Al-Badawi1 , J. H. Asad3 , Mohammed Al-Twiessi1
1 Department of Physics, Al-Hussein Bin Talal University, Ma'an 71111, Jordan2 Department of Physics, Faculty of Sciences, Taibah University, Yanbu, Kingdom of Saudi Arabia3 Department of Physics, Faculty of Arts and Sciences, Palestine Technical University, Kadoorie, Tulkarm, Palestine
Abstract ：The resistance between any two lattice points in an infinite, centered-triangular lattice of equal resistors is determined using the lattice Green function method. It is shown that the two-point resistance on the centered-triangular lattice is expressed in terms of the resistance of a triangular lattice. Some exact values for the resistance near the origin of the lattice are presented. For large separation between lattice points the asymptotic forms of the resistance are calculated.
收稿日期: 2017-09-11
出版日期: 2018-01-23
[1] Jeng M 2000 Am. J. Phys. 68 37 [2] Aitchison R E 1964 Am. J. Phys. 32 566 [3] Venezian G 1994 Am. J. Phys. 62 1000 [4] Atkinson D F and van Steenwijk F J 1999 Am. J. Phys. 67 486 [5] Wu F Y 2004 J. Phys. A Math. Gen. 37 6653 [6] Tan Z Z 2011 Resistor Network Model (Xi'an: Xidian University Press) (in Chinese) [7] Cserti J 2000 Am. J. Phys. 68 896 [8] Cserti J, Szechenyi G and David G 2011 J. Phys. A 44 215201 [9] Owaidat M Q 2013 Am. J. Phys. 81 918 [10] Asad J H 2013 J. Stat. Phys. 150 1177 [11] Owaidat M Q 2014 Appl. Phys. Res. 6 100 [12] Owaidat M Q, Asad J H and Khalifeh J M 2014 Mod. Phys. Lett. B 28 1450252 [13] Owaidat M Q and Asad J H 2016 Eur. Phys. J. Plus 131 309 [14] Asad J H, Diab A A, Owaidat M Q, Hijjawi R S and Khalifeh J M 2014 Acta Phys. Pol. A 125 60 [15] Asad J H, Hijjawi R S, Sakaji A J and Khalifeh J M 2005 Int. J. Mod. Phys. B 19 3713 [16] Owaidat M Q, Hijjawi R S and Khalifeh J M 2014 Eur. Phys. J. Appl. Phys. 68 10102 [17] Asad J H, Diab A A, Owaidat M Q and Khalifeh J M 2014 Acta Phys. Pol. A 126 777 [18] Cserti J, Gyula D and Attila P 2002 Am. J. Phys. 70 153 [19] Owaidat M Q, Hijjawi R S and Khalifeh J M 2010 Mod. Phys. Lett. B 19 2057 [20] Owaidat M Q, Hijjawi R S and Khalifeh J M 2010 J. Phys. A 43 375204 [21] Owaidat M Q, Hijjawi R S and Khalifeh J M 2012 Int. J. Theor. Phys. 51 3152 [22] Owaidat M Q, Hijjawi R S and Khalifeh J M 2014 Eur. Phys. J. Plus 129 29 [23] Owaidat M Q, Asad J H and Tan Z Z 2016 Int. J. Mod. Phys. B Vol. 30 No. 24 1650166 [24] Li B, Wang L and Casati G 2006 Appl. Phys. Lett. 88 143501 [25] Zhang J Q et al 2014 Eur. Phys. J. B 87 122 [26] Zhang J Q et al 2014 Eur. Phys. J. B 87 285 [27] Zhang J Q et al 2016 AIP Adv. 6 075212 [28] Barton G 1989 Elements of Green's Functions and Propagation (Oxford: Oxford University Press) [29] Duffy D G 2001 Green's Functions with Applications (New York: Chapman and Hall/CRC) [30] Economou E 1983 Green's Functions in Quantum Physics (Berlin: Springer-Verlag) [31] Barber M N and Ninham B W 1970 Random and Restricted Walks; Theory and Applications (New York: Gordon and Breach) [32] Hughes B D 1995 Random Walks and Random Environments: Random Walks (Oxford: Clarendon) [33] Wolfram T and Callaway J 1963 Phys. Rev. 130 2207 [34] Syozi I 1972 Transformation of Ising Models (London: Academic Press) vol 1 [35] Kotecky R, Salas J and Sokal A D 2 2008 Phys. Rev. Lett. 101 030601 [36] Chen Q N, Qin, M P, Chen J, Wei Z C, Zhao H H, Normand B and Xiang T 2011 Phys. Rev. Lett. 107 165701 [37] Deng Y J, Huang Y, Jacobsen J L, Salas J and Sokal A D 2011 Phys. Rev. Lett. 107 150601 [38] Azimi-Tafreshi N, Dashti-Naserabadi H, Moghimi-Araghi S and Ruelle P 2010 J. Stat. Mech. P02004
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[8]
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[9]
.
[10]
.
[11]
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[12]
.
[13]
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2018, Vol. 35 
