Quantum critical phenomena in the Schr odinger formulation: mapping to classical lattices

We present a path integral formalism to obtain the statistical mechanics transfer matrix of the system which leads to a straightforward mapping between the quantum problem and an e€ective classical lattice system. Thus, the quantum criticality of atomic and molecular systems can be studied by the standard statistical mechanics methods. We illustrate this general technique by presenting detailed calculations for the screened Coulomb potential. Ó 2001 Elsevier Science B.V. All rights reserved.