arXiv subjects

T. R. Kirkpatrick

Publications and source records attributed to T. R. Kirkpatrick.

151 records · Page 9Linked to original sources

arXiv1997

Quantum ferromagnetic transition in disordered itinerant electron systems

An effective field theory is derived for the ferromagnetic transition of diffusive electrons at T=0. The static disorder which leads to diffusive electron dynamics induces an effective long-range interaction between the spins of the form 1/r^(2d-2). This leads to unusual scaling behavior at the quantum critical point, which is determined exactly. The crossover from this quantum fixed point to the classical Heisenberg fixed point should be observable in ferromagnetic materials with low Curie temperatures.

cond-mat.stat-mech↗

arXiv1994

Order Parameter Description of the Anderson-Mott Transition

An order parameter description of the Anderson-Mott transition (AMT) is given. We first derive an order parameter field theory for the AMT, and then present a mean-field solution. It is shown that the mean-field critical exponents are exact above the upper critical dimension. Renormalization group methods are then used to show that a random-field like term is generated under renormalization. This leads to similarities between the AMT and random-field magnets, and to an upper critical dimension $d_{c}^{+}=6$ for the AMT. For $d<6$, an $ε= 6-d$ expansion is used to calculate the critical exponents. To first order in $ε$ they are found to coincide with the exponents for the random-field Ising model. We then discuss a general scaling theory for the AMT. Some well established scaling relations, such as Wegner's scaling law, are found to be modified due to random-field effects. New experiments are proposed to test for random-field aspects of the AMT.

cond-mat↗

arXiv1994

Density Expansion for the Mobility in a Quantum Lorentz Model

We consider the mobility of electrons in an environment of static hard-sphere scatterers, which provides a realistic description of electrons in Helium gas. A systematic expansion in the scatterer density is carried to second order relative to the Boltzmann result, and the analytic contribution at this order is derived, together with the known logarithmic term in the density expansion. It is shown that existing experimental data are consistent with the existence of the logarithmic term in the density expansion, but more precise experiments are needed in order to unambiguously detect it. We show that our calculations provide the necessary theoretical information for such an experiment, and give a detailed discussion of a suitable parameter range.

cond-mat↗

arXiv1994

The Anderson-Mott Transition as a Random-Field Problem

The Anderson-Mott transition of disordered interacting electrons is shown to share many physical and technical features with classical random-field systems. A renormalization group study of an order parameter field theory for the Anderson-Mott transition shows that random-field terms appear at one-loop order. They lead to an upper critical dimension $d_{c}^{+}=6$ for this model. For $d>6$ the critical behavior is mean-field like. For $d<6$ an $ε$-expansion yields exponents that coincide with those for the random-field Ising model. Implications of these results are discussed.

cond-mat↗

arXiv1994

Density Expansion for the Mobility of Electrons in Helium Gas

We calculate the electron mobility for a quantum Lorentz model, which provides a realistic description of electrons in Helium gas, to second order in the gas density. We show that this provides sufficient theoretical information to allow for an experimental observation of the famous logarithmic term in the density expansion. Detailed predictions, and a discussion of a suitable parameter range, for such an experiment are given.

cond-mat↗

arXiv1994

A Landau Theory for the Metal-Insulator Transition

The nonlinear $σ$-model for disordered interacting electrons is studied in spatial dimensions $d>4$. The critical behavior at the metal-insulator transition is determined exactly, and found to be that of a standard Landau-Ginzburg-Wilson $ϕ^4$-theory with the single-particle density of states as the order parameter. All static exponents have their mean-field values, and the dynamical exponent $z=3$. $\partial n/ \partial μ$ is critical with an exponent of $1/2$, and the electrical conductivity vanishes with an exponent $s=1$. The transition is qualitatively different from the one found in the same model in a $2+ε$ expansion.

cond-mat↗

arXiv1993

The Role of Cooperons in the Disordered Electron Problem: Logarithmic Corrections to Scaling Near the Metal-Insulator Transition

The effect of Cooperons on metal-insulator transitions (MIT) in disordered interacting electronic systems is studied. It is argued that previous results which concluded that Cooperons are qualitatively unimportant near the MIT might not be correct, and that the problem is much more complicated than had previously been realized. Although we do not completely solve the Cooperon problem, we propose a new approach that is at least internally consistent. Within this approach we find that in all universality classes where Cooperons are present, i.e. in the absence of magnetic impurities and magnetic fields, there are logarithmic corrections to scaling at the MIT. This result is used for a possible resolution of the so-called exponent puzzle for the conductivity near the MIT. A discussion of the relationship between theory and experiment is given. We also make a number of predictions concerning crossover effects which occur when a magnetic field is applied to a system with Cooperons.

cond-mat↗