NONEQUILIBRIUM RELAXATION STUDIES FOR FRUSTRATED SPIN SYSTEMS WITH KOSTERLITZ–THOULESS TRANSITIONS

The q-state clock gauge glass model in two dimensions with q = 6, 8, 10, 12, 14, 16 is studied by the use of the nonequilibrium relaxation analysis of the Kosterlitz–Thouless (KT) transition. The successive transitions of FM-KT-PM phases are investigated along the Nishimori line. For the upper critical temperature, it is found that the transition temperature is almost the same as in the continuous case for all q values. The lower transition temperature is found to be proportional to 1/q2. While the present model is not self-dual, we have a remarkable behavior with respect to the duality relation derived for the self-dual Villain-type model.

DISORDERED SUPERCONDUCTORS: A SIMPLE MODEL MANIFESTING PSEUDOGAP AND BCS-BEC CROSSOVER

The effect of random on-site disorder on s-wave (BCS) superconductors described by a two dimensional negative-U Hubbard model is studied using Bogoliubov-de Gennes (BdG) method. The mean field pairing amplitudes become spatially inhomogeneous at large values of disorder where the system breaks up into superconducting islands with large pairing amplitudes, separated by insulating strips. The amplitude fluctuations are correctly accounted for via BdG calculations, however it misses phase fluctuations which are inherent to low dimensions. The phase fluctuations affect superconducting properties strongly, and the effect is more pronounced in the limit of large disorder. We provide a close estimate of the actual transition temperature, Tc by incorporating phase fluctuations about the inhomogeneous BdG state. This is obtained by relating the jump in renormalized Ds (obtained from a self consistent Harmonic approximation on a phase-only Hamiltonian) at the Kosterlitz-Thouless (KT) transition and the KT transition temperature, TKT obtained from Ds(T) = (2/π)TKT as temperature tends to TKT from below. This yields opening of a large region sandwiched between [Formula: see text] (obtained by the vanishing of [Formula: see text]) and TKT where there is no phase coherence between the pairs, however amplitude correlations continue to exist, reminiscent of a pseudogap phase in high-Tc superconductors which is marked by short ranged preformed pairs without any definite phase relation between them. Further, the appearance of the superconducting islands from a homogeneous phase indicates the evolution of a system consisting of large and overlapping pairs to one that contains short and tightly bound pairs - a scenario termed as BCS-BEC crossover. We have investigated in details the crossover phenomenon as a function of disorder and confirmed it's existence at small values of electron concentration, however, absent at larger densities.

Role of Spinon Excitations on KT Transition at Low Energies in d-Wave Superconductors

By using a low energy effective Lagrangian of the U(1) slave boson mean field theory we examine the vortex binding-unbinding transition (KT transition) from a doped Mott insulator at low temperatures in a d-wave superconductor. It is shown that the interaction potential between vortices is modified by a "Doppler energy shift" resulting in additional attractive interaction, as a consequence of supercurrent fluctuations coupled to the particle-hole excitations of the massless Dirac fermions.

SPIKY HIGHER GENUS STRINGS

It is clear from both the non-perturbative and perturbative approaches to two-dimensional quantum gravity that a new strong coupling regime is setting in at d = 1, independent of the genus of the worldsheet being considered. It has been suggested that a Kosterlitz–Thouless (KT) phase transition in the Liouville theory is the cause of this behavior. However, it has recently been pointed out that the XY-model, which displays a KT transition on the plane and the sphere, is always in the strong coupling, disordered phase on a surface of constant negative curvature. A higher genus worldsheet can be represented as a fundamental region on just such a surface, which might seem to suggest that the KT picture predicts a strong coupling region for arbitrary d, contradicting the known results. We resolve the apparent paradox.