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Cluster and virial expansions for the multi-species tonks gas

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posted on 2023-06-09, 04:40 authored by S Jansen
We consider a mixture of non-overlapping rods of different lengths lk moving in R or Z. Our main result are necessary and sufficient convergence criteria for the expansion of the pressure in terms of the activities zk and the densities ?k. This provides an explicit example against which to test known cluster expansion criteria, and illustrates that for non-negative interactions, the virial expansion can converge in a domain much larger than the activity expansion. In addition, we give explicit formulas that generalize the well-known relation between non-overlapping rods and labelled rooted trees. We also prove that for certain choices of the activities, the system can undergo a condensation transition akin to that of the zero-range process. The key tool is a fixed point equation for the pressure.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Journal of Statistical Physics

ISSN

0022-4715

Publisher

Springer Verlag

Issue

5

Volume

161

Page range

1299-1323

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-01-13

First Open Access (FOA) Date

2017-01-13

First Compliant Deposit (FCD) Date

2017-01-13

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