SCHRODINGER INVARIANCE AND STRONGLY ANISOTROPIC CRITICAL SYSTEMS

The extension of strongly anisotropic or dynamical scaling to local scale invariance is investigated. For the special case of an anisotropy or dynamical exponent theta = z = 2, the group of local scale transformation considered is the Schrodinger group, which can be obtained as the nonrelativistic limit of the conformal group. The requirement of Schrodinger invariance determines the two-point function in the bulk and reduces the three-point function to a scaling form of a single variable. Scaling forms are also derived for the two-point function close to a free surface which can be either spacelike or timelike. These results are reproduced in several exactly solvable statistical systems, namely the kinetic Ising model with Glauber dynamics, lattice diffusion, Lifshitz points in the spherical model, and critical dynamics of the spherical model with a non-conserved order parameter. For generic values of theta, evidence from higher-order Lifshitz points in the spherical model and from directed percolation suggests a simple scaling form of the two-point function.