Lars Onsager

Lars Onsager was born in Oslo in 1903 and trained as a chemical engineer at the Norwegian Institute of Technology. In 1925, aged twenty-two, he travelled to Zurich and informed Peter Debye that his celebrated theory of electrolytes was wrong. Debye, to his credit, hired him. Onsager's correction became the Debye–Hückel–Onsager equation, and he moved to the United States in 1928, joining Yale in 1933 — where the faculty discovered he had no doctorate and, after his submitted dissertation proved too difficult for the chemistry department to evaluate, awarded him one anyway.

His reciprocal relations, published in 1931, extended thermodynamics into the irreversible regime for the first time, showing that the cross-coefficients linking coupled flows — heat driving diffusion, a temperature gradient driving an electric current — must be symmetric. The result was so far ahead of its field that it was largely ignored for two decades, until the rise of non-equilibrium thermodynamics made it foundational. It won him the 1968 Nobel Prize in Chemistry.

In 1944 he published the achievement he is best remembered for among physicists: the exact solution of the two-dimensional Ising model at zero field. It is one of the hardest calculations ever completed in the subject — an interacting many-body system above one dimension, solved in closed form with no approximation anywhere — and it found the phase transition Ising had concluded did not exist, at k_BT_c = 2J/ln(1 + √2). More consequentially, its magnetisation vanishes as (T_c − T)^(1/8), the first exact critical exponent ever obtained. The value 1/8, so far from the 1/2 that every mean-field theory predicted, was hard proof that the accepted framework was not merely imprecise but wrong about the shape of a transition; Onsager announced the magnetisation result on a conference blackboard in 1948 and left others to publish the derivation.

Onsager was a famously impenetrable lecturer — his Yale courses were nicknamed 'Sadistical Mechanics' and 'Advanced Norwegian I and II' — and his papers were dense to the point of obstruction. He also predicted quantised vortices in superfluid helium and worked on liquid crystals and colloids. He died in 1976.