Renormalization Group Approach For Systems Research Articles

A new renormalization group approach for systems with strong electron correlation

The anomalous low energy behaviour observed in metals with strong electron correlation, suchas in the heavy fermion materials, is believed to arise from the scattering of the itinerantelectrons with low energy spin fluctuations. In systems with magnetic impurities this scatteringleads to the Kondo effect and a low energy renormalized energy scale, the Kondo temperatureTK. It has been generally assumed that these low energy scales can only be accessed by anon-perturbative approach due to the strength of the local inter-electron interactions. Herewe show that it is possible to circumvent this difficulty by first suppressing the spinfluctuations with a large magnetic field. As a first step field-dependent renormalizedparameters are calculated using standard perturbation theory. A renormalizedperturbation theory is then used to calculate the renormalized parameters for areduced magnetic field strength. The process can be repeated and the flow of therenormalized parameters continued to zero magnetic field. We illustrate the viabilityof this approach for the single impurity Anderson model. The results for therenormalized parameters, which flow as a function of magnetic field, can be checkedwith those from numerical renormalization group and Bethe ansatz calculations.

A non-equilibrium Monte Carlo renormalization-group approach based upon the microscopic master equation applied to the three-state driven lattice gas

We present a general position-space renormalization-group approach for systems in steady states far from equilibrium and illustrate its application to the three-state driven lattice gas. The method is based upon the possibility of a closed form representation of the parameters controlling transition rates of the system in terms of the steady state probability distribution of small clusters, arising from the application of the master equations to small clusters. This probability distribution on various length scales is obtained through a Monte Carlo algorithm on small lattices, which then yields a mapping between parameters on different length scales. The renormalization-group flows indicate the phase diagram, analogous to equilibrium treatments. For the three-state driven lattice gas, we have implemented this procedure and compared the resulting phase diagrams with those obtained directly from simulations. Results in general show the expected topology with one exception. For high densities, an unexpected additional fixed point emerges, which can be understood qualitatively by comparing it with the fixed point of the fully asymmetric exclusion process.

Critical behavior of the ferromagnetic ising chain with interactionJ ij =|i?j|?2

High-temperature expansions of the susceptibility and specific heat are calculated to the eighth and ninth orders, respectively, in the reciprocal temperature for the one-dimensional ferromagnetic Ising model with interaction that decreases inversely as the square of the distance between the lattice sites. An analysis is performed of the expansion of the susceptibility that indicates that at the critical point its logarithm diverges in accordance with a power law exponent. This estimate is close to the value obtained by the renormalization-group method and is the first numerical confirmation of the predictions of the renormalization-group approach for systems with long-range interaction.