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International Symposium on Topological Aspects of Critical Systems and Networks

REAL SPACE RENORMALIZATION GROUP ANALYSIS WITH THE REPLICA METHOD FOR THE TWO-DIMENSIONAL ISING SPIN GLASS

T. HASEGAWA, K. NEMOTO

Published Jun 1, 2007• 0 citations
Publisher
DOI
10.1142/9789812708687_0028

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Using a recently proposed new renormalization group method (tensor renormalization group), we analyze the Ising model on the two-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.