  The interacting symplectic fermion model in two spatial dimensions is further
analyzed. As an effective low energy theory, the model is unitary. We show that
a relativistic mass m is dynamically generated and derive a gap equation for
it. By incorporating a finite temperature we study some fundamental properties
of the model, such as the specific heat and spin response, which clearly show
non-Fermi liquid properties. We find that various physical properties are
suppressed at temperatures T< T* where the cross-over scale is T* = m. As a
simplified, toy model of high Tc superconductivity, we thus identify the
pseudogap energy scale with the zero temperature relativistic mass m, and show
that this reproduces some qualitative aspects of the observed phenomenology of
the pseudogap. The effects of the pseudogap and finite temperature on the
d-wave gap equation are analyzed. In this model, the pseudogap is a distinct
phenomenon from superconductivity and in fact competes with it. Our analysis of
Tc suggests that the quantum critical point of our model, where the pseudogap
vanishes, occurs inside the superconducting dome near optimal doping. For an
antiferromagnetic exchange energy of J/k_B ~ 1350K, solutions of the d-wave gap
equation give a maximum Tc of about 110K.
