Near critical point, correlation length takes a power law behavior (λ-λ_c)^ε, where ε is called critical exponent. Determining the critical exponent is one of essential goals in condensed matter theory, and my work is to determine the critical exponent using standard diagrammatic theory.

Influence of Berry Curvature on Anomalous Hall Effect
Hall effect is the production of current in the direction perpendicular to the electric field applied to a conductor. Normally it needs external magnetic field, however, some materials shows Hall effect without magnetic field. This is called anomalous Hall effect.

Mechanisms for anomalous Hall effect are classified into two, extrinsic mechanisms and intrinsic mechanisms. Extrinsic mechanisms are based on impurity scattering. Hence conductivity depends on relaxation time τ. On the other hand, intrinsic mechanisms depend only on the band sturcutre of material and spin-orbital interaction. Therefore it does not depend on τ.

Recent studies have shown that introducing inhomogeneous magnetic field into Hamiltonian yields Berry phase term in semiclassical equation of motion and the Berry phase term causes anomolous Hall effect. Unfortunately, (or luckily?) temperature dependence of this Berry phase term has not been studied well so far, probably because Berry phase is a geometrical term. However,inhomogeneous magnetization involves domain walls that fluctuate with temperature. I am studying the possibility of temperature dependence of the Berry phase term.