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Balls-in-boxes condensation on networks

L. Bogacz·Z. Burda·W. Janke·B. Waclaw
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Abstract

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 depends on the parameter log(Q/q), which controls the exponential fall-off 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 log(Q/q)=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.

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L. Bogacz, Z. Burda, W. Janke, B. Waclaw. 2007-01-23. Balls-in-boxes condensation on networks. https://doi.org/10.1063/1.2740571

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