Exact real space renormalisation group transformation for the dimerised XY chain
Abstract
An analytical real space renormalisation group transformation is obtained for the onedimensional spin1/2 antiferromagnetic dimerised XY model. Using the method of Sarker (1984) the recursion relations for the parameters are derived from the mapping between blocks of sizes L and L/b, for arbitrary size L and scale factor b. The results for the gap and for the critical exponent are shown to converge rapidly toward their exact values. The dynamical exponent has 1/L corrections (b approximately 1) instead of the usual 1/ln L ones (b=L). The differential renormalisation group equations are obtained explicitly. The authors show that the nonanalyticity of the scaling function (for the density of energy) stems from a dangerous irrelevant variable, the antiferromagnetic coupling.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 December 1986
 DOI:
 10.1088/03054470/19/18/016
 Bibcode:
 1986JPhA...19L1201S