2007/01/23 by L. Bogacz, Z. Burda, Wolfhard Janke +3
Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Condensation #Exponential function #Mathematical analysis #Mathematics #Opinion Dynamics and Social Influence #Partition (number theory) #Partition function (quantum field theory) #Physics #Quantum mechanics #Statics #Statistical physics #Stochastic processes and statistical mechanics #Symmetry breaking #Thermodynamics #cond-mat.other #cond-mat.stat-mech
paper · pdf · doi:10.1063/1.2740571
published as Chaos 17, 026112 (2007) · 7 pages, 3 figures, submitted to the "Chaos" focus issue on "Optimization in Networks" (scheduled to appear as Volume 17, No. 2, 2007)
arxiv created 2007/01/23 · openalex publication_date 2007/06/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We discuss two different regimes of condensate formation in zero-range processes on networks: on a q-regular network, where the condensate is formed as a result of a spontaneous symmetry breaking, and on an irregular network, where the symmetry of the partition function is explicitly broken. In the latter case we consider a minimal irregularity of the q-regular network introduced by a single Q node with degree Q>q. The statics and dynamics of the condensation depend on the parameter alpha=ln Q/q, which controls the exponential falloff of the distribution of particles on regular nodes and the typical time scale for melting of the condensate on the Q node, which increases exponentially with the system size N. This behavior is different than that on a q-regular network, where alpha=0 and where the condensation results from the spontaneous symmetry breaking of the partition function, which is invariant under a permutation of particle occupation numbers on the q nodes of the network. In this case the typical time scale for condensate melting is known to increase typically as a power of the system size.