Seminario Física Teórica

October 29th 2003 -Wednesday- 17,30 h.

"Limit Cycles in the Renormalization Group of the BCS and the sine-Gordon models"

José María Román

We present two models where a different behavior from the standard RG flow to UV or IR fixed points arises, i.e., a cyclic RG flow. We show that a simple extension of the standard BCS Hamiltonian leads to an infinite number of BCS eigenstates with different energy gaps and self-similar properties, described by a cyclic RG flow of the BCS coupling constant which returns to its original value after a finite RG time. A similar RG cyclic behavior is found for a relativistic S-matrix model (extension of the sine-Gordon model) whose scattering is periodic in rapidities. The finite size correction of the free energy $c_{\rm eff}(R)$ oscillates around $c=1$, with a period related to the RG-time of a cycle. References: A. LeClair, J. M. Román and G. Sierra, cond-mat/0211338, to appear in PRB. A. LeClair, J. M. Román and G. Sierra, hept-th/0301042, to appear in NPB.

Seminario de Física Atómica, Molecular y Nuclear Facultad de Ciencias, 1rd Floor, Universidad de Zaragoza