I worked with Barry Simon and Jürg Fröhlich and what we wanted to do was provide rigorous proofs that three dimensional ferromagnets had phase transitions under very general conditions, and we really weren't able to do it, and we never achieved what we set out to do, and I haven't followed the subject. I think Fröhlich has done a lot more since. I don't regard that as a glorious chapter in my history. I don't think I've much to say about it. I mean, the problems again are purely mathematical and we ran into difficulties which didn't seem to be physically motivated, I mean, seemed to be just simply we hadn't found the right tools, somehow, to deal with them, and so I don't think it's worth talking about that really. Just... we had a certain degree of success, we were able to prove quite interesting results but under very restricted conditions, which obviously ought to hold much more generally.

[Q] What I had in mind actually was your work, which you entitled 'hierarchical models' and you had mentioned earlier the influence of Besicovitch in how to solve problems, and here was a case where Besicovitch's approach was useful in structuring, in modelling a system and giving a mathematical proof?

Yes. That was of course connected with the one dimensional ferromagnets which I spoke about already. I mean the point was, the hierarchical model is a analytically solvable model, so that it has interactions which have a much higher degree of symmetry than the one dimensional chain. And the hierarchical model is not actually one dimensional. But the point is that you can map the hierarchical model into a one dimensional chain in such a way that the interactions in the one dimensional chain are always larger than the interactions in the hierarchical model. So you get inequalities, so that the binding in the one dimensional chain is stronger than it is in the hierarchical model, so you can get very useful information about the one dimensional chain by solving the hierarchical model. So the hierarchical model was in the Besicovitch style; it was a mathematical tool with which to deal with the physical case. It worked beautifully, and it turns out, of course, once you've invented the hierarchical model you can study it as an object in itself. It has very interesting properties. I was... I invented it actually just as an analytical tool in order to deal with the one dimensional chain.