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Edge Spectrum for Truncated (mathbb {Z}_2)-Insulators 截断(mathbb {Z}_2)绝缘子的边缘谱
IF 1.1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2025-08-23 DOI: 10.1007/s11040-025-09520-4
Alexis Drouot, Jacob Shapiro, Xiaowen Zhu
{"title":"Edge Spectrum for Truncated (mathbb {Z}_2)-Insulators","authors":"Alexis Drouot,&nbsp;Jacob Shapiro,&nbsp;Xiaowen Zhu","doi":"10.1007/s11040-025-09520-4","DOIUrl":"10.1007/s11040-025-09520-4","url":null,"abstract":"<div><p>Fermionic time-reversal-invariant insulators in two dimension – class AII in the Kitaev table – come in two different topological phases. These are characterized by a <span>(mathbb {Z}_2)</span>-invariant: the Fu–Kane–Mele index. We prove that if two such insulators with different indices occupy regions containing arbitrarily large balls, then the spectrum of the resulting operator fills the bulk spectral gap. Our argument follows a proof by contradiction developed in [16] for quantum Hall systems. It boils down to showing that the <span>(mathbb {Z}_2)</span>-index can be computed only from bulk information in sufficiently large balls. This is achieved via a result of independent interest: a local trace formula for the <span>(mathbb {Z}_2)</span>-index.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multi-component discrete integrable hierarchy and its Hamiltonian structure 多分量离散可积层次及其哈密顿结构
IF 1.1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2025-08-22 DOI: 10.1007/s11040-025-09523-1
Haifeng Wang, Zhenzhu Fang, Jian Li, Chuanzhong Li
{"title":"Multi-component discrete integrable hierarchy and its Hamiltonian structure","authors":"Haifeng Wang,&nbsp;Zhenzhu Fang,&nbsp;Jian Li,&nbsp;Chuanzhong Li","doi":"10.1007/s11040-025-09523-1","DOIUrl":"10.1007/s11040-025-09523-1","url":null,"abstract":"<div><p>We introduce a kind of infinite-dimensional Lie algebra, it follows that a scheme for generating multi-component discrete integrable hierarchy of soliton equations is proposed. A multi-component discrete quadratic-form identity is presented which could be used to establish Hamiltonian structures of multi-component discrete integrable hierarchies. By considering the application, we obtain a coupled and a multi-component Volterra lattice hierarchies and their Liouville integrable Hamiltonian structures.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deformations of Clarke–Oliveira Instantons on Bryant–Salamon Spin(7)-Manifold Bryant-Salamon自旋(7)流形上Clarke-Oliveira瞬子的变形
IF 1.1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2025-08-20 DOI: 10.1007/s11040-025-09522-2
Tathagata Ghosh
{"title":"Deformations of Clarke–Oliveira Instantons on Bryant–Salamon Spin(7)-Manifold","authors":"Tathagata Ghosh","doi":"10.1007/s11040-025-09522-2","DOIUrl":"10.1007/s11040-025-09522-2","url":null,"abstract":"<div><p>In this paper we compute the deformations of the Clarke–Oliveira instantons on the Bryant–Salamon <i>Spin</i>(7)-Manifold. The Bryant–Salamon <i>Spin</i>(7)-Manifold — the negative spinor bundle of <span>(S^4)</span> — is an asymptotically conical manifold where the link is the squashed 7-sphere. We use the deformation theory developed by the author in a previous paper to calculate the deformations of the Clarke–Oliveira instantons and calculate the virtual dimensions of the moduli spaces.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144880862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Trigonometric-type Hirota–Miwa equation 三角型Hirota-Miwa方程
IF 1.1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2025-08-08 DOI: 10.1007/s11040-025-09519-x
Ya-Jie Liu, Hui Alan Wang, Xing-Biao Hu, Ying-Nan Zhang
{"title":"The Trigonometric-type Hirota–Miwa equation","authors":"Ya-Jie Liu,&nbsp;Hui Alan Wang,&nbsp;Xing-Biao Hu,&nbsp;Ying-Nan Zhang","doi":"10.1007/s11040-025-09519-x","DOIUrl":"10.1007/s11040-025-09519-x","url":null,"abstract":"<div><p>The Hirota–Miwa equation is one of the most celebrated fully discrete integrable systems. By introducing bilinear operators of trigonometric-type, we propose a novel variant of the Hirota–Miwa equation, which can be regarded as an integrable discretization of the Kadomtsev–Petviashvili-I (KPI) equation. It turns out that this new equation admits a number of physically significant solutions, including solitons, lumps, breathers, and periodic wave solutions. As far as we know, it is the first time that lump solutions have been reported in the context of fully discrete integrable systems. In addition, the numerical periodic wave solutions are computed by employing deep learning techniques. Finally, the reduction procedure is considered, which yields a trigonometric-type discrete Korteweg–de Vries (KdV) equation and a trigonometric-type discrete Boussinesq equation.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Power-law correction in the probability density function of the critical Ising magnetization 临界伊辛磁化的概率密度函数的幂律修正
IF 1.1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2025-08-06 DOI: 10.1007/s11040-025-09517-z
Federico Camia, Omar El Dakkak, Giovanni Peccati
{"title":"Power-law correction in the probability density function of the critical Ising magnetization","authors":"Federico Camia,&nbsp;Omar El Dakkak,&nbsp;Giovanni Peccati","doi":"10.1007/s11040-025-09517-z","DOIUrl":"10.1007/s11040-025-09517-z","url":null,"abstract":"<div><p>At the critical point, the probability density function of the Ising magnetization is believed to decay like <span>(exp {(-x^{delta +1})})</span>, where <span>(delta )</span> is the Ising critical exponent that controls the decay to zero of the magnetization in a vanishing external field. In this paper, we discuss the presence of a power-law correction <span>(x^{frac{delta -1}{2}})</span>, which has been debated in the physics literature. We argue that whether such a correction is present or not is related to the asymptotic behavior of a function that measures the extent to which the average magnetization of a finite system with an external field is influenced by the boundary conditions. Our discussion is informed by a mixture of heuristic calculations and rigorous results. Along the way, we review some recent results on the critical Ising model and prove properties of the average magnetization in two dimensions which are of independent interest.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-025-09517-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Evolution of Discordance 不和谐的进化
IF 1.1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2025-08-06 DOI: 10.1007/s11040-025-09518-y
F. den Hollander
{"title":"Evolution of Discordance","authors":"F. den Hollander","doi":"10.1007/s11040-025-09518-y","DOIUrl":"10.1007/s11040-025-09518-y","url":null,"abstract":"<div><p>The present paper is a brief overview of random opinion dynamics on random graphs based on the Ising Lecture given by the author at the World Congress in Probability and Statistics, 12–16 August 2024, Bochum, Germany. The content is a snapshot of an interesting area of research that is developing rapidly.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-025-09518-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Ising model: highlights and perspectives 伊辛模型：亮点和视角
IF 1.1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2025-08-02 DOI: 10.1007/s11040-025-09515-1
Christof Külske
{"title":"The Ising model: highlights and perspectives","authors":"Christof Külske","doi":"10.1007/s11040-025-09515-1","DOIUrl":"10.1007/s11040-025-09515-1","url":null,"abstract":"<div><p>We give a short non-technical introduction to the Ising model, and review some successes as well as challenges which have emerged from its study in probability and mathematical physics. This includes the infinite-volume theory of phase transitions, and ideas like scaling, renormalization group, universality, SLE, and random symmetry breaking in disordered systems and networks. This note is based on a talk given on 15 August 2024, as part of the Ising lecture during the 11th Bernoulli-IMS world congress, Bochum.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-025-09515-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Translation-invariant p-adic generalized Gibbs measures for the Ising model with a homogeneous external field on a Cayley tree Cayley树上齐次外场Ising模型的平移不变p进广义Gibbs测度
IF 1.1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2025-07-30 DOI: 10.1007/s11040-025-09516-0
Zulxumor Abdukaxorova
{"title":"Translation-invariant p-adic generalized Gibbs measures for the Ising model with a homogeneous external field on a Cayley tree","authors":"Zulxumor Abdukaxorova","doi":"10.1007/s11040-025-09516-0","DOIUrl":"10.1007/s11040-025-09516-0","url":null,"abstract":"<div><p>This paper investigates translation-invariant <i>p</i>-adic generalized Gibbs measures for the <i>p</i>-adic Ising model with a homogeneous external field on a Cayley tree of order three, assuming <span>(p &gt; 3)</span>. We demonstrate that if <span>(p equiv 1 (operatorname {mod} {6}))</span>, then there exist four translation-invariant <i>p</i>-adic generalized Gibbs measures; if <span>(p not equiv 1 (operatorname {mod} {6}))</span>, there exist exactly two. Additionally, for any prime <span>(p &gt; 3)</span>, we establish the occurrence of a phase transition in this model.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exploring Metastability in Ising models: critical droplets, energy barriers and exit time 探索Ising模型中的亚稳态：临界液滴、能量势垒和退出时间
IF 1.1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2025-07-24 DOI: 10.1007/s11040-025-09514-2
Vanessa Jacquier
{"title":"Exploring Metastability in Ising models: critical droplets, energy barriers and exit time","authors":"Vanessa Jacquier","doi":"10.1007/s11040-025-09514-2","DOIUrl":"10.1007/s11040-025-09514-2","url":null,"abstract":"<div><p>This paper provides an overview of the research on the metastable behaviour of the Ising model. We analyse the transition times from the set of metastable states to the set of the stable states by identifying the critical configurations that the system crosses with high probability during this transition and by computing the energy barrier that the system must overcome to reach the stable state starting from the metastable one. We describe the dynamical phase transition of the Ising model evolving under Glauber dynamics across various contexts, including different lattices, dimensions and anisotropic variants. The analysis is extended to related models, such as long-range Ising model, Blume-Capel and Potts models, as well as to dynamics like Kawasaki dynamics, providing insights into metastability across different systems.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-025-09514-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Locations of JNR Skyrmions JNR skyrmins的位置
IF 1.1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2025-07-11 DOI: 10.1007/s11040-025-09513-3
Josh Cork, Linden Disney–Hogg
{"title":"Locations of JNR Skyrmions","authors":"Josh Cork,&nbsp;Linden Disney–Hogg","doi":"10.1007/s11040-025-09513-3","DOIUrl":"10.1007/s11040-025-09513-3","url":null,"abstract":"<div><p>We develop and prove new geometric and algebraic characterisations for locations of constituent skyrmions, as well as their signed multiplicity, using Sutcliffe’s JNR ansatz. Some low charge examples, and their similarity to BPS monopoles, are discussed. In addition, we provide Julia code for the further numerical study and visualisation of JNR skyrmions.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-025-09513-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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