Mathematical Physics

Pacific Journal of Mathematics1261987
MathReview: 93e:82028
Lecture Notes in Physics447Springer Verlag1994
MathReview: 94e:82056
Advances in Mathematical Sciences: CRM's 25 Years1991
MathReview: 95d:60161

Author's comments: There are two papers on the Bethe Ansatz, but the work is far from complete. I have always wanted to return not only to the algebraic geometrical arguments initiated in the second paper, which seem to me of considerable intrinsic mathematical interest as algebraic geometry, but also to the notion of Wellenkomplex and the Puiseux expansions introduced briefly at the end of the first paper. So far, I have not found the time.

Appeared in Twenty years of Bialowieza: A Mahtematical anthology, World Scientific Monograph Series in Mathematics8

Author's comments: This paper was prepared for a meeting in Bialowieza that I was unable at the last minute to attend. It has appeared in the proceedings of that conference, Twenty years of Bialowieza: A mathematical anthology. The paper was intended as a beginning. Several years of work, largely numerical and very often in collaboration, on percolation and the Ising model were an attempt on my part to get a handle on what was for me their mathematically fascinating aspect, referred to as renormalization: the observed behavior of large systems for which repeated re-scaling is possible can be described by a very small number of parameters, and the convergence under re-scaling of the values of these parameters to their limits is extremely rapid. I have never found in the literature or discovered on my own any method of any general promise for defining these parameters or for demonstrating their properties. I had hoped when writing this paper to have within my grasp some promising ideas. I thought about them, but either I did not think long enough or hard enough, or they were worth less than I thought. Whatever it was, my attention has been distracted for several years by other matters, every bit as difficult and intractable as renormalization, so that I have not been able to return to it. This was likely no loss to science, but I regret it, for the mathematical questions are in my view of profound interest. I still harbor a little hope that in the coming years I can return to them.