Renormalization Group Theory: Impact on Experimental Magnetism

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		Renormalization Group Theory: Impact on Experimental Magnetism
		Renormalization Group Theory: Impact on Experimental Magnetism

Spin wave theory of magnetism and BCS theory of superconductivity are typical theories of the time before renormalization group (RG) theory. The two theories consider atomistic interactions only and ignore the energy degrees of freedom of the continuous (infinite) solid. Since the pioneering work of Kenneth G. Wilson (Nobel Prize of physics in 1982) we know that the continuous solid is characterized by a particular symmetry: invariance with respect to transformations of the length scale. Associated with this symmetry are particular field particles with characteristic excitation spectra. In diamagnetic solids these are the well known Debye bosons. This book reviews experimental work on solid state physics of the last five decades and shows in a phenomenological way that the dynamics of ordered magnets and conventional superconductors is controlled by the field particles of the infinite solid and not by magnons and Cooper pairs, respectively. In the case of ordered magnets the relevant field particles are called GSW bosons after Goldstone, Salam and Weinberg and in the case of superconductors the relevant field particles are called SC bosons. One can imagine these bosons as magnetic density waves or charge density waves, respectively. Crossover from atomistic exchange interactions to the excitations of the infinite solid occurs because the GSW bosons have generally lower excitation energies than the atomistic magnons. According to the principle of relevance the dynamics is governed by the excitations with the lowest energy. The non relevant atomistic interactions with higher energy are practically unimportant for the dynamics.

History of Conventional Spin Wave Theory.- Basic Issues of Renormalization Group (RG) Theory.- Universality.- Microscopic Processes.- Non-Relevant Magnons.- Crossover Phenomena.- Metastability of Universality Classes.- Relevant and Non-Relevant Interactions.- Temperature Dependence of the Magnon Excitation Spectra.- Magnetic Heat Capacity.- Experimental Verification of GSW Bosons.- Magnets With and Without Magnon Gap (Goldstone Mode).- Microscopic Details: Spin Structure, Site Disorder, Two Order Parameters.- The Critical Magnetic Behaviour.- Thermal Lattice Expansion and Magnetostriction.- The Total Energy Content.- Superconductivity.- Conclusions.

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The title of this book, "Renormalization Group Theory", published in a books series of the renowned science publisher Springer Verlag, may sound appealing to the prospective reader desiring to acquire some knowledge on renormalization group theory and its implications for magnetic systems.

Unfortunately, the content of the book is light-years away from what its title suggests. In particular, it does not contain any exposition of renormalization group theory. Instead, the authors offer their (very) personal views on the physics of magnetic excitations at low temperatures in ferro- and antiferromagnetic systems. The "theory" proposed by the authors is motivated by their experimental observations, which they find to be in disagreement with predictions of spin-wave theory. While there is probably not much to object to their experimental body of work, the theoretical interpretation the authors offer for their observations is a complete nonsense. The authors apparently use words and concepts of theoretical physics in a loose manner without understanding them and without being able to construct any rational, physically any mathematically sound, reasoning. In particular, the authors try to construct an incomprehensible and fully unjustified distinction between spin-waves and Goldstone bosons, upon which they build up all kinds of arbitrary claims, such as the existence of "universality classes", but they apparently ignore or fail to understand that the spin-waves are precisely the Goldstone bosons of magnetically ordered systems (see for example "Quantum Field Theory in Condensed Matter Physics" by N. Nagaosa (Springer Verlag, 1999)).

With exception of the experimental data, which are presumably collected in an honest and competent manner, but moderately interesting per se, this 400 pages-thick book can be best described as a pseudo-scientific publication. It is in fact extremely disturbing to see it being published by a publisher of the reputation of Springer Verlag.

To conclude, the prospective reader with some keen interest in renormalization group theory or in magnetism is strongly advised not to waste his/her money on this pseudo-scientific book.

Patrick Bruno
Head of Theory Group
European Synchrotron Radiation Facility, Grenoble, France

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