CRITICAL-BEHAVIOR OF ELECTRONIC PARQUET SOLUTIONS

The "basic" parquet equations for lattice electron models are shown to predict the same critical exponents eta that follow from a self-consistent 1/N expansion for the corresponding order-parameter field theories. The approximate exponents are correct through terms of O(1/N), with N the number of order-parameter components. In two dimensions, the parquet equations correctly predict the presence of a finite-temperature phase transition for Ising-like systems and the absence of such a transition for Heisenberg-like systems. The behavior of xy-like systems remains an open question.