Renormalization-group study of interfacial properties and its applications to an Ising spin glass

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Abstract
Studies of the critical phenomena of interfaces have been made using the Migdal-Kadanoff transformation for the Ising, three-state Potts, Blume-Emery-Griffiths, XY, and Ising-spin-glass models. We examine scaling relationships as a function of temperature or coupling and system size. In particular, we examine the implications of this transformation for rcolation. We find t=1.29±0.03 for the lattice and t=1.34±0.07 for the continuum, in agreement with a recent theoretical prediction that the conductivity exponents for these two systems are the same. We have also verified a theoretical estimate of the magnitude of conductance fluctuations due to finite-size effects.