Godrèche, Claude Comment on: “Fluctuation-dominated phase ordering at a mixed order transition”. (English) Zbl 1519.82038 J. Phys. A, Math. Theor. 54, No. 3, Article ID 038001, 8 p. (2021). Summary: Renewal processes generated by a power-law distribution of intervals with tail index less than unity are genuinely non-stationary. This issue is illustrated by a critical review of the recent paper by M. Barma et al. [J. Phys. A, Math. Theor. 52, No. 25, Article ID 254001, 20 p. (2019; Zbl 1509.82094)], devoted to the investigation of the properties of a specific one-dimensional equilibrium spin system with long-range interactions. We explain why discarding the non-stationarity of the process underlying the model leads to an incorrect expression of the critical spin-spin correlation function, even when the system, subjected to periodic boundary conditions, is translation invariant. Cited in 1 ReviewCited in 2 Documents MSC: 82B26 Phase transitions (general) in equilibrium statistical mechanics 60K05 Renewal theory Keywords:non-stationarity; renewal processes; power-law tails Citations:Zbl 1509.82094 PDFBibTeX XMLCite \textit{C. Godrèche}, J. Phys. A, Math. Theor. 54, No. 3, Article ID 038001, 8 p. (2021; Zbl 1519.82038) Full Text: DOI arXiv References: [1] Barma M, Majumdar S N and Mukamel D 2019 J. Phys. A: Math. Theor.52 254001 · Zbl 1509.82094 [2] Thouless D J 1969 Phys. Rev.187 732 [3] Anderson P W, Yuval G and Hamann D R 1970 Phys. Rev. B 1 4464 [4] Aizenman M, Chayes J T, Chayes L and Newman C M 1988 J. Stat. Phys.50 1 · Zbl 1084.82514 [5] Bar A and Mukamel D 2014 Phys. Rev. Lett.112 015701 [6] Bar A and Mukamel D 2014 J. Stat. Mech. P11001 · Zbl 1456.82337 [7] Bar A, Majumdar S N, Schehr G and Mukamel D 2016 Phys. Rev.93 052130 [8] Godrèche C 2017 J. Stat. Mech. 073205 · Zbl 1456.60210 [9] Godrèche C 2017 J. Phys. A: Math. Theor.50 195003 · Zbl 1371.60075 [10] Godrèche C 2020 J. Stat. Phys. (at press) arXiv:2006.04076 [cond-mat.stat-mech] [11] Wendel J G 1964 Math. Scand.14 21 · Zbl 0132.12802 [12] Bialas P, Burda Z and Johnston D 1999 Nucl. Phys. B 542 413 · Zbl 0953.83003 [13] Fisher M E 1984 J. Stat. Phys.34 667 · Zbl 0589.60098 [14] Cox D R 1962 Renewal Theory (London: Methuen) · Zbl 0103.11504 [15] Godrèche C and Luck J M 2001 J. Stat. Phys.104 489 · Zbl 0985.60094 [16] Bouchaud J-P and Dean D S 1995 J. Phys. I France5 265 [17] Das D and Barma M 2000 Phys. Rev. Lett.85 1602 [18] Das D, Barma M and Majumdar S N 2001 Phys. Rev. E 64 046126 [19] Barma M, Majumdar S N and Mukamel D 2019 arXiv:1902.06416v1 [cond-mat.stat-mech] [20] Godrèche C 2019 arXiv:1909.11540 [cond-mat.stat-mech] [21] Godrèche C in preparation This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.