We suggest a new mean field method for studying the thermodynamic competition
between magnetic and superconducting phases in a two-dimensional square
lattice. A partition function is constructed by writing microscopic
interactions that describe the exchange of density and spin-fluctuations. A
block structure dictated by spin, time-reversal, and bipartite symmetries is
imposed on the single-particle Hamiltonian. The detailed dynamics of the
interactions are neglected and replaced by a normal distribution of random
matrix elements. The resulting partition function can be calculated exactly.
The thermodynamic potential has a structure which depends only on the spectrum
of quasiparticles propagating in fixed condensation fields, with coupling
constants that can be related directly to the variances of the microscopic
processes. The resulting phase diagram reveals a fixed number of phase
topologies whose realizations depend on a single coupling-parameter ratio,
alpha. Most phase topologies are realized for a broad range of values of alpha
and can thus be considered robust with respect to moderate variations in the
detailed description of the underlying interactions.Comment: 21 pages, 8 figures, RevTex 4. Minor grammatical errors corrected in
the last versio
