{"title":"忽略了伊辛模型的Berezin解","authors":"M. Ostilli","doi":"10.1140/epjh/s13129-025-00093-y","DOIUrl":null,"url":null,"abstract":"<div><p>In 1969, the Russian Mathematical Survey published a paper by Felix A. Berezin called “THE PLANE ISING MODEL” (Berezin in Russ Math Surv 24:1, 1969) where Onsager’s solution of the two-dimensional Ising model is found by means of integrals over anticommuting variables (Grassmann variables). Berezin’s work provides a very elegant method for solving the Ising model which turns out to be much simpler if compared to previous methods. Berezin’s work represents also the very first use of anticommuting variables for solving actual combinatorial problems. Western literature, however, has ignored Ref. Berezin (Russ Math Surv 24:1, 1969). In fact, more than a decade after Berezin’s paper, S. Samuel re-found, independently, essentially the same solution obtained by Berezin, but with no reference to his work. S. Samuel solved also other planar models and paved the way to a subsequent proliferation of papers both related to statistical mechanics and fermionic field theories. Yet, we have verified that, until now, western literature still does not cite the original work of Berezin on the Ising model. The aim of this perspective paper is to fix this chronic issue and contextualize it within the unfortunate biographical and historical facts around Berezin’s life.</p></div>","PeriodicalId":791,"journal":{"name":"The European Physical Journal H","volume":"50 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The ignored Berezin’s solution of the Ising model\",\"authors\":\"M. Ostilli\",\"doi\":\"10.1140/epjh/s13129-025-00093-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In 1969, the Russian Mathematical Survey published a paper by Felix A. Berezin called “THE PLANE ISING MODEL” (Berezin in Russ Math Surv 24:1, 1969) where Onsager’s solution of the two-dimensional Ising model is found by means of integrals over anticommuting variables (Grassmann variables). Berezin’s work provides a very elegant method for solving the Ising model which turns out to be much simpler if compared to previous methods. Berezin’s work represents also the very first use of anticommuting variables for solving actual combinatorial problems. Western literature, however, has ignored Ref. Berezin (Russ Math Surv 24:1, 1969). In fact, more than a decade after Berezin’s paper, S. Samuel re-found, independently, essentially the same solution obtained by Berezin, but with no reference to his work. S. Samuel solved also other planar models and paved the way to a subsequent proliferation of papers both related to statistical mechanics and fermionic field theories. Yet, we have verified that, until now, western literature still does not cite the original work of Berezin on the Ising model. The aim of this perspective paper is to fix this chronic issue and contextualize it within the unfortunate biographical and historical facts around Berezin’s life.</p></div>\",\"PeriodicalId\":791,\"journal\":{\"name\":\"The European Physical Journal H\",\"volume\":\"50 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-02-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The European Physical Journal H\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1140/epjh/s13129-025-00093-y\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"HISTORY & PHILOSOPHY OF SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal H","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjh/s13129-025-00093-y","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}
引用次数: 0
摘要
1969年,俄罗斯数学调查发表了Felix a . Berezin的一篇论文,名为“the PLANE ISING MODEL”(Berezin In Russ Math Surv 24:1, 1969),其中通过对反交换变量(Grassmann变量)的积分找到了二维ISING模型的Onsager解。Berezin的工作为解决伊辛模型提供了一种非常优雅的方法,与以前的方法相比,这种方法要简单得多。Berezin的工作也是第一次使用反交换变量来解决实际的组合问题。然而,西方文学忽略了Ref. Berezin (Russ Math Surv 24:1, 1969)。事实上,在别列津的论文发表十多年后,S. Samuel独立地重新发现了与别列津得到的基本相同的解,但没有提及他的工作。塞缪尔还解决了其他平面模型,并为随后与统计力学和费米子场论相关的论文的激增铺平了道路。然而,我们已经证实,直到现在,西方文献仍然没有引用别列津关于伊辛模型的原始著作。这篇透视论文的目的是解决这个长期问题,并将其置于别列津生活中不幸的传记和历史事实中。
In 1969, the Russian Mathematical Survey published a paper by Felix A. Berezin called “THE PLANE ISING MODEL” (Berezin in Russ Math Surv 24:1, 1969) where Onsager’s solution of the two-dimensional Ising model is found by means of integrals over anticommuting variables (Grassmann variables). Berezin’s work provides a very elegant method for solving the Ising model which turns out to be much simpler if compared to previous methods. Berezin’s work represents also the very first use of anticommuting variables for solving actual combinatorial problems. Western literature, however, has ignored Ref. Berezin (Russ Math Surv 24:1, 1969). In fact, more than a decade after Berezin’s paper, S. Samuel re-found, independently, essentially the same solution obtained by Berezin, but with no reference to his work. S. Samuel solved also other planar models and paved the way to a subsequent proliferation of papers both related to statistical mechanics and fermionic field theories. Yet, we have verified that, until now, western literature still does not cite the original work of Berezin on the Ising model. The aim of this perspective paper is to fix this chronic issue and contextualize it within the unfortunate biographical and historical facts around Berezin’s life.
期刊介绍:
The purpose of this journal is to catalyse, foster, and disseminate an awareness and understanding of the historical development of ideas in contemporary physics, and more generally, ideas about how Nature works.
The scope explicitly includes:
- Contributions addressing the history of physics and of physical ideas and concepts, the interplay of physics and mathematics as well as the natural sciences, and the history and philosophy of sciences, together with discussions of experimental ideas and designs - inasmuch as they clearly relate, and preferably add, to the understanding of modern physics.
- Annotated and/or contextual translations of relevant foreign-language texts.
- Careful characterisations of old and/or abandoned ideas including past mistakes and false leads, thereby helping working physicists to assess how compelling contemporary ideas may turn out to be in future, i.e. with hindsight.