In this work, we study a model, first proposed and solved by Sutherland, of N fermions on a line which interact through a sinh^-2(r) pairwise potential. This model is integrable and its thermodynamics can be obtained through asymptotic Bethe Ansatz method. The aim of this work is to reinterpret the system as one made of free particles obeying a so-called fractional statistics.

In chapter 1, we make a quick review of Bethe Ansatz method and quantum integrability and then present Haldane's definition of fractional statistics with all the thermodynamics induced by it. In chapter 2, we present the model, prove its integrability and solve it using asymptotic Bethe Ansatz. In chapter 3, we derive the thermodynamics of the system using fractional statistics and we show that the interaction can be seen as a statistical one.