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

Authors

Fangfang Wang, Wei Liu, Kai Qi, Zidong Cui, Ying Tang, Zengru Di

Published in

Physical review. E. Volume 114. Issue 3-1. Pages 034118.

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.

PMID:
42888809
Bibliographic data and abstract were imported from PubMed on 17 Oct 2026.

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