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Phase Transitions for a Class of Time-Inhomogeneous Diffusion Processes

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Abstract

In this paper, we study phase transitions of a class of time-inhomogeneous diffusion processes associated with the \(\varphi ^4\) model. We prove that when \(\gamma <0\), the system has no phase transition and when \(\gamma >0\), the system has a phase transition and we study the phase transition of the system through qualitative and quantitative methods. We further show that, as the strength of the mean field tends to 0, the solution and stationary distribution of such system converge locally uniformly in \(L^2\) and Wasserstein distance respectively to those of corresponding system without mean field.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (11931004, 12090011) and the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Author notes

  1. Yao Liu and Yingchao Xie have contributed equally to this work.

Authors and Affiliations

  1. School of Mathematics and Statistics, Fujian Normal University, South Xuefu Road 8, Fuzhou, 350007, Fujian, China

    Yao Liu & Mengge Zhang

  2. Research Institute of Mathematical Science and School of Mathematics and Statistics, Jiangsu Normal University, Shanghai Road 101, Xuzhou, 221116, Jiangsu, China

    Yingchao Xie

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  1. Yao Liu
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Correspondence to Mengge Zhang.

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Communicated by Li-Cheng Tsai.

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The original online version of this article was revised: In this article the affiliation details for Yingchao Xie were incorrect and it has been updated.

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Liu, Y., Xie, Y. & Zhang, M. Phase Transitions for a Class of Time-Inhomogeneous Diffusion Processes. J Stat Phys 190, 42 (2023). https://doi.org/10.1007/s10955-022-03054-7

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