Communications in Mathematical Physics最新文献

{"title":"Percolation for 2D Classical Heisenberg Model and Exit Sets of Vector Valued GFF","authors":"Juhan Aru,&nbsp;Christophe Garban,&nbsp;Avelio Sepúlveda","doi":"10.1007/s00220-024-05208-y","DOIUrl":"10.1007/s00220-024-05208-y","url":null,"abstract":"<div><p>Our motivation in this paper is twofold. First, we study the geometry of a class of exploration sets, called <i>exit sets</i>, which are naturally associated with a 2D vector-valued Gaussian Free Field : <span>(phi : mathbb {Z}^2 rightarrow mathbb {R}^N, Nge 1)</span>. We prove that, somewhat surprisingly, these sets are a.s. degenerate as long as <span>(Nge 2)</span>, while they are conjectured to be macroscopic and fractal when <span>(N=1)</span>. This analysis allows us, when <span>(Nge 2)</span>, to understand the percolation properties of the level sets of <span>({ Vert phi (x)Vert _{{2}}, xin mathbb {Z}^2})</span> and leads us to our second main motivation in this work: if one projects a spin <span>(O(N+1))</span> model (the case <span>(N=2)</span> corresponds to the classical Heisenberg model) down to a spin <i>O</i>(<i>N</i>) model, we end up with a spin <i>O</i>(<i>N</i>) in a quenched disorder given by random conductances on <span>(mathbb {Z}^2)</span>. Using the <i>exit sets</i> of the <i>N</i>-vector-valued GFF, we obtain a local and geometric description of this random disorder in the limit <span>(beta rightarrow infty )</span>. This allows us in particular to revisit a series of celebrated works by Patrascioiu and Seiler (J Stat Phys 69(3):573–595, 1992, Nucl Phys B Proc Suppl 30:184–191, 1993, J Stat Phys 106(3):811–826, 2002) which argued against Polyakov’s prediction that spin <span>(O(N+1))</span> model is massive at all temperatures as long as <span>(Nge 2)</span> (Polyakov in Phys Lett B 59(1):79–81, 1975). We make part of their arguments rigorous and more importantly we provide the following counter-example: we build ergodic environments of (arbitrary) high conductances with (arbitrary) small and disconnected regions of low conductances in which, despite the predominance of high conductances, the <i>XY</i> model remains massive. Of independent interest, we prove that at high <span>(beta )</span>, the fluctuations of a classical Heisenberg model near a north pointing spin are given by a <span>(N=2)</span> vectorial GFF. This is implicit for example in Polyakov (1975) but we give here the first (non-trivial) rigorous proof. Also, independently of the recent work Dubédat and Falconet (Random clusters in the villain and xy models, arXiv preprint arXiv:2210.03620, 2022), we show that two-point correlation functions of the spin <i>O</i>(<i>N</i>) model can be given in terms of certain percolation events in the <i>cable graph</i> for any <span>(Nge 1)</span>.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05208-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Linear Inviscid Damping in the Presence of an Embedding Eigenvalue","authors":"Siqi Ren,&nbsp;Zhifei Zhang","doi":"10.1007/s00220-024-05209-x","DOIUrl":"10.1007/s00220-024-05209-x","url":null,"abstract":"<div><p>In this paper, we investigate the long-time dynamics of the linearized 2-D Euler equations around a hyperbolic tangent flow <span>((tanh y,0))</span>. A key difference compared with previous results is that the linearized operator has an embedding eigenvalue, which has a significant impact on the dynamics of the linearized system. For the first mode, the dynamics consist of there parts: non-decay part related to the eigenspace associated with the embedding eigenvalue, slow decay part due to the resolvent singularity, and fast decay part related to the inviscid damping. For higher modes, the dynamic is similar to the inviscid damping phenomena in the case without embedding eigenvalues.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Spectra of the Gravity Water Waves Linearized at Monotone Shear Flows","authors":"Xiao Liu,&nbsp;Chongchun Zeng","doi":"10.1007/s00220-024-05219-9","DOIUrl":"10.1007/s00220-024-05219-9","url":null,"abstract":"<div><p>We consider the spectra of the 2-dim gravity waves of finite depth linearized at a uniform monotonic shear flow <span>(U(x_2))</span>, <span>(x_2 in (-h, 0))</span>, where the wave numbers <i>k</i> of the horizontal variable <span>(x_1)</span> is treated as a parameter. Our main results include a.) a complete branch of non-singular neutral modes <span>(c^+(k))</span> strictly decreasing in <span>(kge 0)</span> and converging to <i>U</i>(0) as <span>(k rightarrow infty )</span>; b.) another branch of non-singular neutral modes <span>(c_-(k))</span>, <span>(k in (-k_-, k_-))</span> for some <span>(k_-&gt;0)</span>, with <span>(c_-(pm k_-) = U(-h))</span>; c.) the non-degeneracy and the bifurcation at <span>((k_-, c=U(-h)))</span>; d.) the existence and non-existence of unstable modes for <i>c</i> near <i>U</i>(0), <span>(U(-h))</span>, and interior inflection values of <i>U</i>; e.) the complete spectral distribution in the case where <span>(U'')</span> does not change sign or changes sign exactly once non-degenerately. In particular, <i>U</i> is spectrally stable if <span>(U'U''le 0)</span> and unstable if <i>U</i> has a non-degenerate interior inflection value or <span>({U'U''&gt;0})</span> accumulate at <span>(x_2=-h)</span> or 0. Moreover, if <i>U</i> is an unstable shear flow of the fixed boundary problem in a channel, then strong gravity could cause instability of the linearized gravity waves in all long waves (i.e. <span>(|k|ll 1)</span>).</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of Approximately Macroscopically Unique States","authors":"Huaxin Lin","doi":"10.1007/s00220-024-05218-w","DOIUrl":"10.1007/s00220-024-05218-w","url":null,"abstract":"<div><p>Let <i>H</i> be an infinite dimensional separable Hilbert space and <i>B</i>(<i>H</i>) the <span>(C^*)</span>-algebra  of bounded operators on <i>H</i>. Suppose that <span>(T_1,T_2,..., T_n)</span> are self-adjoint operators in <i>B</i>(<i>H</i>). We show that, if commutators <span>([T_i, T_j])</span> are sufficiently small in norm, then “Approximately Macroscopically Unique\" states always exist for any values in a synthetic spectrum of the <i>n</i>-tuple of self-adjoint operators. This is achieved under the circumstance for which the <i>n</i>-tuple may not be approximated by commuting ones. This answers a question proposed by David Mumford for measurements in quantum theory. If commutators are not small in norm but small modulo compact operators, then “Approximate Macroscopic Uniqueness\" states also exist.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Large N von Neumann Algebras and the Renormalization of Newton’s Constant","authors":"Elliott Gesteau","doi":"10.1007/s00220-024-05192-3","DOIUrl":"10.1007/s00220-024-05192-3","url":null,"abstract":"<div><p>I derive a family of Ryu–Takayanagi formulae that are valid in the large <i>N</i> limit of holographic quantum error-correcting codes, and parameterized by a choice of UV cutoff in the bulk. The bulk entropy terms are matched with a family of von Neumann factors nested inside the large <i>N</i> von Neumann algebra describing the bulk effective field theory. These factors are mapped onto one another by a family of conditional expectations, which are interpreted as a renormalization group flow for the code subspace. Under this flow, I show that the renormalizations of the area term and the bulk entropy term exactly compensate each other. This result provides a concrete realization of the ER=EPR paradigm, as well as an explicit proof of a conjecture due to Susskind and Uglum.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantum Broadcast Channel Simulation via Multipartite Convex Splitting","authors":"Mario Berta,&nbsp;Hao-Chung Cheng,&nbsp;Li Gao","doi":"10.1007/s00220-024-05191-4","DOIUrl":"10.1007/s00220-024-05191-4","url":null,"abstract":"<div><p>We show that the communication cost of quantum broadcast channel simulation under free entanglement assistance between the sender and the receivers is asymptotically characterized by an efficiently computable single-letter formula in terms of the channel’s multipartite mutual information. Our core contribution is a new one-shot achievability result for multipartite quantum state splitting via multipartite convex splitting. As part of this, we face a general instance of the quantum joint typicality problem with arbitrarily overlapping marginals. The crucial technical ingredient to sidestep this difficulty is a conceptually novel multipartite mean-zero decomposition lemma, together with employing recently introduced complex interpolation techniques for sandwiched Rényi divergences. Moreover, we establish an exponential convergence of the simulation error when the communication costs are within the interior of the capacity region. As the costs approach the boundary of the capacity region moderately quickly, we show that the error still vanishes asymptotically.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05191-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Some Simple Orbifold Affine VOAs at Non-admissible Level Arising from Rank One 4D SCFTs","authors":"Tomoyuki Arakawa,&nbsp;Xuanzhong Dai,&nbsp;Justine Fasquel,&nbsp;Bohan Li,&nbsp;Anne Moreau","doi":"10.1007/s00220-024-05196-z","DOIUrl":"10.1007/s00220-024-05196-z","url":null,"abstract":"<div><p>We study the representations of some simple affine vertex algebras at non-admissible level arising from rank one 4D SCFTs. In particular, we classify the irreducible highest weight modules of <span>(L_{-2}(G_2))</span> and <span>(L_{-2}(B_3))</span>. It is known by the works of Adamović and Perše that these vertex algebras can be conformally embedded into <span>(L_{-2}(D_4))</span>. We also compute the associated variety of <span>(L_{-2}(G_2))</span>, and show that it is the orbifold of the associated variety of <span>(L_{-2}(D_4))</span> by the symmetric group of degree 3 which is the Dynkin diagram automorphism group of <span>(D_4)</span>. This provides a new interesting example of associated variety satisfying a number of conjectures in the context of orbifold vertex algebras.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142962955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"B-Twisted Gaiotto–Witten Theory and Topological Quantum Field Theory","authors":"Niklas Garner,&nbsp;Nathan Geer,&nbsp;Matthew B. Young","doi":"10.1007/s00220-024-05211-3","DOIUrl":"10.1007/s00220-024-05211-3","url":null,"abstract":"<div><p>We develop representation theoretic techniques to construct three dimensional non-semisimple topological quantum field theories which model homologically truncated topological B-twists of abelian Gaiotto–Witten theory with linear matter. Our constructions are based on relative modular structures on the category of weight modules over an unrolled quantization of a Lie superalgebra. The Lie superalgebra, originally defined by Gaiotto and Witten, is associated to a complex symplectic representation of a metric abelian Lie algebra. The physical theories we model admit alternative realizations as Chern–Simons–Rozansky–Witten theories and supergroup Chern–Simons theories and include as particular examples global forms of <span>(mathfrak {gl}(1 vert 1))</span>-Chern–Simons theory and toral Chern–Simons theory. Fundamental to our approach is the systematic incorporation of non-genuine line operators which source flat connections for the topological flavour symmetry of the theory.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Magnetic Flatness and E. Hopf’s Theorem for Magnetic Systems","authors":"Valerio Assenza,&nbsp;James Marshall Reber,&nbsp;Ivo Terek","doi":"10.1007/s00220-024-05166-5","DOIUrl":"10.1007/s00220-024-05166-5","url":null,"abstract":"<div><p>Using the notion of magnetic curvature recently introduced by the first author, we extend E. Hopf’s theorem to the setting of magnetic systems. Namely, we prove that if the magnetic flow on the <i>s</i>-sphere bundle is without conjugate points, then the total magnetic curvature is non-positive, and vanishes if and only if the magnetic system is magnetically flat. We then prove that magnetic flatness is a rigid condition, in the sense that it only occurs when either the magnetic form is trivial and the metric is flat, or when the magnetic system is Kähler, the metric has constant negative sectional holomorphic curvature, and <i>s</i> equals the Mañé critical value.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05166-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"First Passage Percolation, Local Uniqueness for Interlacements and Capacity of Random Walk","authors":"Alexis Prévost","doi":"10.1007/s00220-024-05195-0","DOIUrl":"10.1007/s00220-024-05195-0","url":null,"abstract":"<div><p>The study of first passage percolation (FPP) for the random interlacements model has been initiated in Andres and Prévost (Ann Appl Probab 34(2):1846–1895), where it is shown that on <span>(mathbb {Z}^d)</span>, <span>(dge 3)</span>, the FPP distance is comparable to the graph distance with high probability. In this article, we give an asymptotically sharp lower bound on this last probability, which additionally holds on a large class of transient graphs with polynomial volume growth and polynomial decay of the Green function. When considering the interlacement set in the low-intensity regime, the previous bound is in fact valid throughout the near-critical phase. In low dimension, we also present two applications of this FPP result: sharp large deviation bounds on local uniqueness of random interlacements, and on the capacity of a random walk in a ball.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05195-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142962948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}