  Using a recently proposed new renormalization group method (tensor
renormalization group), we analyze the Ising model on the 2-dimensional square
lattice. For the lowest order approximation with two domain wall states, it
realizes the idea of coarse graining of domain walls. We write down explicit
analytic renormalization transformation and prove that the picture of the
coarse graining of the physical domain walls does hold for all physical
renormalization group flows. We solve it to get the fixed point structure and
obtain the critical exponents and the critical temperature. These results are
very near to the exact values. We also briefly report the improvement using
four domain wall states.
