Random energy model and the replica method

I will talk about the random energy model (REM) and its relevance to disordered non-equilibrium systems such as disordered ZRP and TASEP processes. The REM began life as a very simple model of a spin glass and has proved relevant to a number of different areas including the glass transition, optimisation problems and models of financial systems. It shows a rich structure of free energy minima connected to replica symmetry breaking. I will show how its properties can be obtained using simple statistical arguments and how the replica method can be used to explore the free energy landscape.