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Phase transition in a stochastic geometry model with applications to statistical mechanics
  • O. Kazemi,
  • A. Pourdarvish,
  • J. Sadeghi
O. Kazemi
University of Mazandaran
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A. Pourdarvish
University of Mazandaran
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J. Sadeghi
University of Mazandaran
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Abstract

We study the connected components of the stochastic geometry model on Poisson points which is obtained by connecting points with a probability that depends on their relative position. Equivalently, we investigate the random clusters of the ran- dom connection model defined on the points of a Poisson process in d-dimensional space where the links are added with a particular probability function. We use the thermodynamicrelationsbetweenfreeenergy,entropyandinternalenergytofindthe functions of the cluster size distribution in the statistical mechanics of extensive and non-extensive. By comparing these obtained functions with the probability function predicted by Penrose, we provide a suitable approximate probability function. More- over, we relate this stochastic geometry model to the physics literature by showing how the fluctuations of the thermodynamic quantities of this model correspond to other models when a phase transition (10.1002/mma.6965, 2020) occurs. Also, we obtain the critical point using a new analytical method.
18 Dec 2021Submitted to Mathematical Methods in the Applied Sciences
22 Dec 2021Submission Checks Completed
22 Dec 2021Assigned to Editor
30 Dec 2021Reviewer(s) Assigned
11 Mar 2022Review(s) Completed, Editorial Evaluation Pending
12 Mar 2022Editorial Decision: Revise Major
15 Mar 20221st Revision Received
16 Mar 2022Submission Checks Completed
16 Mar 2022Assigned to Editor
16 Mar 2022Reviewer(s) Assigned
25 Mar 2022Review(s) Completed, Editorial Evaluation Pending
03 May 2022Editorial Decision: Accept