The 2021 Three Physicists Prize is awarded to Marc Mézard for his outstanding work in statistical physics, in particular on the theory of spin glasses and the theory of disordered systems.
After a thesis on the mean field theory of spin glasses, Marc Mézard, Giorgio Parisi and Miguel Virasoro develop an interpretation of these vitreous phases by introducing the cavity method which reproduces, in a physically clear manner, the results of replica symmetry breaking. In this method, we consider the effect of a frozen disorder on an additional spin, a kind of recurrence on the number of degrees of freedom. Marc Mézard establishes a direct relationship between replica symmetry breaking and aging, a characteristic of disordered systems.
The remarkable book by Mézard, Parisi, Virasoro “Spin glass theory and beyond” published in 1987 had a profound influence on the development of the subject and led mathematicians (in particular M. Talagrand) to take an interest in the problem and finally demonstrate that the free energy of a spin glass calculated by physicists was correct.
More recently, Marc Mézard and his collaborators have applied the concepts developed for spin glasses to algorithmic problems, for example the theory of “satisfiability” for a system governed by a certain number of random clauses for Boolean variables. They also discuss the study of statistics of rare or extreme events, in particular in the financial field. Thus, the work of Marc Mézard, initially purely fundamental, allowed major advances in other disciplines, in particular in algorithms, combinatorial optimization and Artificial Intelligence.