Statistical mechanics of multipartite entanglement
  We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions. We search for those (maximally multipartite entangled) states whose purity is minimum for all bipartitions and recast this optimization problem into a problem of statistical mechanics. 
Paolo Facchi, Giuseppe Florio, Ugo Marzolino, Giorgio Parisi, Saverio   Pascazio