With his collaborators, he showed how all the experimental data then available for the changes, called second-order phase transitions, could be understood in terms of these two ideas.

He exploited mathematical analogies between solid state physics and urban growth to shed insights into the latter field, so much so that he contributed substantially to the statewide planning program in Rhode Island.

During the last decade, he has received the Quantrell Award (for excellence in teaching) from the University of Chicago, the Centennial Medal of Harvard University, the Lars Onsager Prize of the American Physical Society, and the Grande Medaille d'Or of the Académie des sciences de l'Institut de France.

His textbook with Gordon Baym, Quantum Statistical Mechanics (ISBN 020141046X), is a prominent text in the field and has been widely translated.

In June 2013, it was stated that anonymous donors had provided a $3.5 million gift to establish the Leo Kadanoff Center for Theoretical Physics at the University of Chicago.