Abstract
We use symmetry to find the mean-field states that can arise at a continuous transition from the normal phase in a two-dimensional itinerant Heisenberg model on a square lattice with unit cell a\ifmmode\times\else\texttimes\fi{}a. All states consistent with a \ensuremath{\surd}2 a\ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}2 a unit cell for both ferromagnetic and antiferromagnetic couplings of the exchange constant are considered. A sublattice SU(2) symmetry is used to map between particle-hole and particle-particle states, charge and singlet-pairing states, and spin and triplet-pairing states. We calculate the critical temperatures for these states and find, at weak coupling, a spin-current state that has a higher critical temperature than the ferromagnetic state.
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