The ignored Berezin’s solution of the Ising model

Abstract

In 1969, the Russian Mathematical Survey published a paper by Felix A. Berezin called “THE PLANE ISING MODEL” (Berezin in Russ Math Surv 24:1, 1969) where Onsager’s solution of the two-dimensional Ising model is found by means of integrals over anticommuting variables (Grassmann variables). Berezin’s work provides a very elegant method for solving the Ising model which turns out to be much simpler if compared to previous methods. Berezin’s work represents also the very first use of anticommuting variables for solving actual combinatorial problems. Western literature, however, has ignored Ref. Berezin (Russ Math Surv 24:1, 1969). In fact, more than a decade after Berezin’s paper, S. Samuel re-found, independently, essentially the same solution obtained by Berezin, but with no reference to his work. S. Samuel solved also other planar models and paved the way to a subsequent proliferation of papers both related to statistical mechanics and fermionic field theories. Yet, we have verified that, until now, western literature still does not cite the original work of Berezin on the Ising model. The aim of this perspective paper is to fix this chronic issue and contextualize it within the unfortunate biographical and historical facts around Berezin’s life.