Exact solution for the superconducting transition in one dimension

Leonard W. Gruenberg, Leon Gunther

DAVID J. ROWE, C. Bahri, Wasantha Wijesundera

We consider a many-fermion model which exhibits a transition from a superconducting to a rotational phase with variation of a parameter in its Hamiltonian. The model has analytical solutions in its two limits due to the presence of dynamical symmetries. However, the symmetries are basically incompatible with one another; no simple solution exists in intermediate situations. Exact (numerical) solutions are possible and enable one to study the behavior of competing but incompatible symmetries and the phase transitions that result in a semirealistic situation. The results are remarkably simple and shed light on the nature of phase transitions.

R. W. Gibberd

The partition function and the Gibb's free energy are calculated exactly in the thermodynamic limit, using techniques which are well known in the theory of superconductivity. This calculation illustrates explicitly the similarity between the phase transition in superconductivity and the molecular field transitions in spin systems.

J. Zittartz, Andreas Klümper, Andreas Schadschneider +1 more

Андрей Георгиевич Семенов, Andrei D. Zaikin

Élliott H. Lieb, Fa Yueh Wu