Real-space renormalization-group approach to the random transverse-field Ising model in finite dimensions

Ryoji Miyazaki, Hidetoshi Nishimori

Published 2012-10-18, updated 2013-06-14Version 2

The transverse-field Ising models with random exchange interactions in finite dimensions are investigated by means of a real-space renormalization-group method. The scheme yields the exact values of the critical point and critical exponent nu in one dimension and some previous results in the case of random ferromagnetic interactions are reproduced in two and three dimensions. We apply the scheme to spin glasses in transverse fields in two and three dimensions, which have not been analyzed very extensively. The phase diagrams and the critical exponent nu are obtained and evidence for the existence of an infinite-randomness fixed point in these models is found.