Renormalization of the hopping parameters in quasi-one-dimensional conductors in the presence of a magnetic field

We consider the competition between the one dimensionalization effect due to a magnetic field and the hopping parameters in quasi-one-dimensional conductors. Our study is based on a perturbative renormalization group method with three cut-off parameters, the bandwidth E0, the 1D-2D crossover temperature T*1, which is related to the hopping process t1, and the magnetic energy \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\omega_c$\end{document}. We have found that the renormalized crossover temperatures T*1 and T*2, at which the respectively hopping processes t1 and t2 become coherent, are reduced compared to the bare values as the field is increased. We discuss the consequences of these renormalization effects on the temperature-field phase diagram of the organic conductors.