Ising, mathematical physicist

Ising was a student of Lenz, and he showed that the classical spin model now called the Ising model did not give rise to any phase transitions in one dimension. Peierls realised that in two dimensions, it does predict a spontaneous (=ferromagnetic) transition. This marked a turning point in physics; before Peierls's argument, there was a strong faction among physicists who argued that one could not use the same variables to describe a material in the solid phase as those needed in the liquid phase. Thus, in the crystal solid phase, we describe a material by the displacement of each atomic site from its equilibrium position; in the liquid phase, we use density of particles and velocity fields as the variables. Ergo, one should not have ambitions to be able to predict phase transitions. Peierls led the way, to describe a system by its microvariables in both phases.