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Real Space Renormalization Group (RSRG) treatment of Ising model for squareand simple cubic lattice is investigated and critical coupling strengths ofthese lattices are obtained. The mathematical complications, which appearinevitable in the decimated partition function due to Block-spintransformation, is treated with a relevant approximation. The approximation isbased on the approximate equivalence of $\ln(1+f(K,\{\sigma_{n.n}\})) \simeqf(K,\{\sigma_{n.n}\})$ for small $f(K,\{\sigma_{n.n}\})$, here $K$ is thenearest neighbor coupling strength and $\{\sigma_{n.n}\}$ is the nearestneighbor spins degrees of freedom around a central spin. The values of thecritical coupling strengths are obtained as $0.4830$ for square lattice and$0.2225$ for simple cubic (SC) lattice. The corresponding critical exponentsvalues $\alpha$ and $\nu$ are also calculated within very acceptable agreementwith those values obtained from numerical works.

A New Approach to Real Space Renormalization Group Treatment of Ising Model for Square and Simple Cubic Lattice