Research Projects

In this proposed research project, I would like to investigate the role of long-range interactions near the quantum critical point of second-order phase transitions observed in itinerant ferromagnets. We thus write down an effective Ginzburg-Landau theory for bosonic order-parameter with nonlocal quartic couplings. We develop a nonlocal renormalization-group formalism along the line of the Hertz-Millis-Moriya (HMM) theory. We determine the condition in which integrating out hidden variables leads to the expected anomalous contribution to the interaction vertices. By solving the one-loop renormalization-group equations, one can have a different regime of phase space corresponding to the fixed points of the theory. We expect a stable Gaussian behavior leading to the existence of a tricritical point before the quantum critical point is reached. We further analyze the long-range behavior and find the anomalous Fisher's scaling leading to the continuous varying universality classes in such itinerant electron systems. Our theoretical framework might provide valuable information about the role of long-range coupling on first-order instability that leads to a tricritical point. We also find continuous varying universality classes observed in various itinerant electron systems due to long-range interactions.