The exact evaluation of the corner-to-corner resistance of an M x N resistor network: Asymptotic expansion

Abstract

We study the corner-to-corner resistance of an M x N resistor network with resistors r and s in the two spatial directions, and obtain an asymptotic expansion of its exact expression for large M and N. For M = N, r = s =1, our result is R_{NxN} = (4/pi) log N + 0.077318 + 0.266070/N^2 - 0.534779/N^4 + O(1/N^6).

12 pages, re-arranged sections

References in corpus (2)

• Theory of resistor networks: The two-point resistance
• Exact Finite-Size Scaling and Corrections to Scaling in the Ising Model with Brascamp-Kunz Boundary Conditions

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