the BCS approximation. The method is applied to the t− t′ Hubbard model in two
dimensions with the following results:(i) The superconducting phase diagram at half filling is
shown to provide a weak-coupling analog of the recently proposed spin liquid state in the J
1− J 2 Heisenberg model.(ii) In the parameter region relevant for the cuprates, we have
found a nontrivial energy dependence of the gap function in the dominant d-wave pairing …