RESUMO
We study the equilibrium and dynamical properties of the axial next-nearest-neighbor Ising chain at the multiphase point. An interesting property of the system is the macroscopic degeneracy of the ground state leading to finite zero-temperature entropy. In our equilibrium study we consider the effect of softening the spins. We show that the degeneracy of the ground state is lifted and there is a qualitative change in the low-temperature behavior of the system with a well-defined low-temperature peak of the specific heat that carries the thermodynamic "weight" of the ground state entropy. In our study of the dynamical properties, the stochastic Kawasaki dynamics is considered. The Fokker-Planck operator for the process corresponds to a quantum spin Hamiltonian similar to the Heisenberg ferromagnet but with constraints on allowed states. This leads to a number of differences in its properties, which are obtained through exact numerical diagonalization, simulations, and by obtaining various analytic bounds.
RESUMO
We present the exact solution of a model of interacting fermions in any dimension with a pure repulsive interaction projecting out a given Cooper channel. The solution rests upon the infinite ranged character of the interaction in real space, leading to a functional integral that is dominated by a Gaussian term. The solution produces strong superconducting enhancements and quasi-long-ranged order in a channel that is not present in the Hamiltonian explicitly, but of the form given by arguments from order by projection.
