Breaking of ensemble equivalence for complex networks
For many system in statistical physics the microcanonical and canonical ensemble are equivalent in the thermodynamic limit, but not for all.
- Roccaverde, A.
- 05 December 2018
- Thesis in Leiden Repository
For many system in statistical physics the microcanonical and canonical ensemble are equivalent in the thermodynamic limit, but not for all. The goal is to classify for which classes of complex networks with topological constraints, breaking of ensemble equivalence occurs. We consider the simple case in which we fix the number of links and then we move to the configuration model (we fix the degree of each vertex). Then we study a more general setting with an arbitrary number of intra-connected and inter-connected layers, thus allowing modular graphs with a community structure. We give a full classication of ensemble equivalence in the sparse and dense regime, proving that break-down occurs when the number of constrained degrees is extensive in the number of nodes, irrespective of the layer structure. In addition, we derive an explicit formula for the specific relative entropy and provide an interpretation of this formula in terms of Poissonisation of the degrees.We also prove that breaking of ensemble equivalence may occur also when the number of constraints is finite but frustrated.