34 research outputs found
The one dimensional Kondo lattice model at partial band filling
The Kondo lattice model introduced in 1977 describes a lattice of localized
magnetic moments interacting with a sea of conduction electrons. It is one of
the most important canonical models in the study of a class of rare earth
compounds, called heavy fermion systems, and as such has been studied
intensively by a wide variety of techniques for more than a quarter of a
century. This review focuses on the one dimensional case at partial band
filling, in which the number of conduction electrons is less than the number of
localized moments. The theoretical understanding, based on the bosonized
solution, of the conventional Kondo lattice model is presented in great detail.
This review divides naturally into two parts, the first relating to the
description of the formalism, and the second to its application. After an
all-inclusive description of the bosonization technique, the bosonized form of
the Kondo lattice hamiltonian is constructed in detail. Next the
double-exchange ordering, Kondo singlet formation, the RKKY interaction and
spin polaron formation are described comprehensively. An in-depth analysis of
the phase diagram follows, with special emphasis on the destruction of the
ferromagnetic phase by spin-flip disorder scattering, and of recent numerical
results. The results are shown to hold for both antiferromagnetic and
ferromagnetic Kondo lattice. The general exposition is pedagogic in tone.Comment: Review, 258 pages, 19 figure
Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries
How Agency Can Solve Interventionism's Problem of Circularity
Contains fulltext :
122781.pdf (publisher's version ) (Open Access)Woodwardâs interventionist theory of causation is beset by a problem of circularity: the analysis of causes is in terms of interventions, and the analysis of interventions is in terms of causes. This is not in itself an argument against the correctness of the analysis. But by requiring us to have causal knowledge prior to making any judgements about causation, Woodwardâs theory does make it mysterious how we can ever start acquiring causal knowledge. We present a solution to this problem by showing how the interventionist notion of causation can be rationally generated from a more primitive agency notion of causation. The agency notion is easily and non-circularly applicable, but fails when we attempt to capture causal relations between non-actions. We show that the interventionist notion of causation serves as an appropriate generalisation of the agency notion. Furthermore, the causal judgements based on the latter generally remain true when rephrased in terms of the former, which allows one to use the causal knowledge gained by applying the agency notion as a basis for applying Woodwardâs interventionist theory. We then present an overview of relevant empirical evidence from developmental psychology which shows that our proposed rational reconstruction lines up neatly with the actual development of causal reasoning in children. This gives additional plausibility to our proposal. The article thus provides a solution to one of the main problems of interventionism while keeping Woodwardâs analysis intact.23 november 201