International Journal of Modern Physics B Vol. 21, No. 2 (2007) 199–209 c  World Scientiﬁc Publishing Company PERTURBATION OF AN INFINITE NETWORK OF IDENTICAL CAPACITORS R. S. HIJJAWI * , J. H. ASAD †, § , A. J. SAKAJI ‡ and J. M. KHALIFEH † * Department of Physics, Mutah University, Jordan † Department of Physics, University of Jordan, Amman-11942, Jordan ‡ Department of Physics, Ajman University, UAE § jihadasd2002@yahoo.com. Received 18 March 2006 The capacitance between any two arbitrary lattice sites in an inﬁnite square lattice is studied when one bond is removed (i.e. perturbed). A connection is made between the capacitance and the lattice Green’s function of the perturbed network, where they are expressed in terms of those of the perfect network. The asymptotic behavior of the perturbed capacitance is investigated as the separation between the two sites goes to in- ﬁnity. Finally, numerical results are obtained along diﬀerent directions and a comparison is made with the perfect capacitances. Keywords : Lattice Green’s function; capacitors; perturbed lattice. 1. Introduction The calculation of the resistance of an inﬁnite network of identical resistors is a classic well-studied problem in the electric circuit theory. 1–3 Despite this, the above-mentioned problem is still of interest and it brings the attention of many authors 4–6 to study and investigate it. At the beginning of this century, this problem arose again in many publica- tions. 7,8 The methods used in studying this problem vary from superposition of current distribution, 4,5 random walk theory 6 and lattice Green’s function (LGF) method. 7,8 In a recent work, the problem for many lattices for both the perfect and per- turbed cases using Cserti’s 7,8 method has been studied: (i) Asad 9 and Asad et al. 10 studied the perfect and perturbed (i.e. where one bond is removed) square and simple cubic (SC) inﬁnite lattices mathematically and experimentally. There was a good agreement between the mathematical and the experimental results, especially for the bulk values. Also, there was a good § Corresponding author. 199