So... at the beginning of last month I posted about a plan to take one of the books I have on my physics bookshelf each month and do something worthwhile with it - learn something that I didn't know, work through some problem and see what enlightenment I get, even kick-start a research project, and then report back here with what I've learnt.
The first book, as prompted by a post on X (a website I have left in favour of BlueSky), was Ashcroft and Mermin's weighty textbook on Solid State Physics. I should preface this whole post by saying that I'm a bit disappointed (with myself) for not carefully managing my time to get more out of the book, but, you know, life. It's been probably a busier September than most years. It's the one year that all 4 of my kids are in school, with the youngest starting Reception Year and the oldest in Year 13, and its freshers flu season, and all sorts of other reasons ... I got "promoted" to be the representative of nuclear physics at STFC's science board at very short notice and that knocked out a couple of days.
Well, so much for the excuses. What about the book?
I picked up a copy of the book when I was a PhD student, bought from Oxford's Blackwell's bookshop. There's still a sticker on the back of the book telling me that I paid £25.95 for it, which even in the late 90s was not a bad price for a hefty 800-page hardback advanced-level textbook. Despite the pretty poor rate of the PhD stipend in those days, it was the first time in my life I felt rich enough to splash out £26 on textbooks. My PhD was not in Solid State Physics but I recognised it as an interesting area that I understood to be a ripe area for a would-be theoretical physics to do a PhD in. Probably it was foolish of me to go fo nuclear physics over solid state, but I had largely found the teaching of Solid State physics uninspiring as an undergraduate and had not been motivated to learn very much of it, and felt ill-prepared for further study. Well, I bought the textbook to have as a reference and perhaps I thought I'd even study it and learn from it, an indication that I was not as self-aware then as I am now. Or at least I saw a practically endless life with copious spare time stretching in front of me in a way I don't now.
Picking up the book now, I started by reading from the beginning with the Drude Theory of Metals - a picture in which mobile electrons form a gas following the laws of kinetic theory. The theory dates back to only just after the discovery of the electron, but before the structure of atoms was understood, and before the laws of quantum mechanics, so vital for atomic and solid state structure so generally, were known. As a model it does a reasonable job (order of magnitude or better) of giving free electron densities and resistivities of metals; it can describe the Hall effect, and thermal conductivity. The Drude model was something I had studied once upon a time, but I would have been hard pressed to say anything about it now, before re-learning from Ashcroft and Mermin.
I carried on skimming through the following chapters to get an idea of the broad brush of development of ideas, but then decided that I wanted to learn at least something that might be a bit more useful to me, so I jumped way ahead to near the end of the book, to the chapter on Electron Interactions and Magnetic Structure. It contains introductions to the kinds of spin Hamiltonians familar as standard models to me as a quantum many-body physicist: the Heisenberg model and the Hubbard model. I realise I had a very facile view of the development of these models, supposing that they started from the assumptions that you could imagine lattices in atoms with magnetic moments were fixed in place and you supposed a very simple interaction between the atoms based on the relative orientation of the neighbouring spins. In reality, there is much more to it, and this is brought out nicely in the book. For a start, though they are models of magnetism, the authors emphasise the electrostatic origin of the magnetic effects. Mainly because of the required antisymmetry of the overall wave function, the spin orientation of atoms in a lattice can be determined, with the spin having to match (or "anti-match", I suppose) with the spatial part of the wave function, which itself is determined mainly by electrostatic effects. Actual magnetic interactions between atoms are a smaller effect when it comes to how the atoms line up to give macroscopic magnetism. Interesting!
Of course, I would have liked to have gone further, and worked through some examples to do actual calculations, and maybe worked through a problem or two at the end of the chapters. I am already a week late writing this up here, though, and a week late starting the October book, so alas I will leave A&M behind for now. On the other hand, I have to submit some ideas for BSc final year projects for Physics students at Surrey, so maybe I'll set one on the Heisenberg model, and vicariously live my continuing interest in this stuff through my student.
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| To my regret, this exercise resulted in a nasty splodge on the fore-edge of the book when I left it in my bag with a too-ripe banana. Still, perhaps that's better than having the book look pristine through being barely touched since its purchase nearly 30 years ago |
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