Communications in Mathematical Physics最新文献

{"title":"Shattering in Pure Spherical Spin Glasses","authors":"Ahmed El Alaoui,&nbsp;Andrea Montanari,&nbsp;Mark Sellke","doi":"10.1007/s00220-025-05243-3","DOIUrl":"10.1007/s00220-025-05243-3","url":null,"abstract":"<div><p>We prove the existence of a shattered phase within the replica-symmetric phase of the pure spherical <i>p</i>-spin models for <i>p</i> sufficiently large. In this phase, we construct a decomposition of the sphere into well-separated small clusters, each of which has exponentially small Gibbs mass, yet which together carry all but an exponentially small fraction of the Gibbs mass. We achieve this via quantitative estimates on the derivative of the Franz–Parisi potential, which measures the Gibbs mass profile around a typical sample. Corollaries on dynamics are derived, in particular, we show the two-times correlation function of stationary Langevin dynamics must have an exponentially long plateau. We further show that shattering implies disorder chaos for the Gibbs measure in the optimal transport sense; this is known to imply failure of sampling algorithms which are stable under perturbation in the same metric.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143821776","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":"A Heterotic Hermitian–Yang–Mills Equivalence","authors":"Jock McOrist,&nbsp;Sebastien Picard,&nbsp;Eirik Eik Svanes","doi":"10.1007/s00220-025-05272-y","DOIUrl":"10.1007/s00220-025-05272-y","url":null,"abstract":"<div><p>We consider <span>(N=1)</span>, <span>(d=4)</span> vacua of heterotic theories in the large radius limit in which <span>({{alpha }^{backprime },}ll 1)</span>. We construct a real differential operator <span>(mathcal {D}= D+bar{D})</span> on an extension bundle <span>((Q, mathcal {D}))</span> with underlying topology <span>(Q=(T^{1,0}X)^* oplus textrm{End} , E oplus T^{1,0} X)</span> whose curvature is holomorphic and Hermitian–Yang–Mills with respect to the complex structure and metric on the underlying non-Kähler complex 3-fold <i>X</i> if and only if the heterotic supersymmetry equations and Bianchi identity are satisfied. This is suggestive of an analogue of the Donaldson–Uhlenbeck–Yau correspondence for heterotic vacua of this type.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05272-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809369","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":"Oscillatory Motions, Parabolic Orbits and Collision Orbits in the Planar Circular Restricted Three-Body Problem","authors":"José Lamas,&nbsp;Marcel Guardia,&nbsp;Tere M. Seara","doi":"10.1007/s00220-025-05283-9","DOIUrl":"10.1007/s00220-025-05283-9","url":null,"abstract":"<div><p>In this paper we consider the planar circular restricted three body problem (PCRTBP), which models the motion of a massless body under the attraction of other two bodies, the primaries, which describe circular orbits around their common center of mass. In a suitable system of coordinates, this is a two degrees of freedom Hamiltonian system. The orbits of this system are either defined for all (future or past) time or eventually go to collision with one of the primaries. For orbits defined for all time, Chazy provided a classification of all possible asymptotic behaviors, usually called final motions. By considering a sufficiently small mass ratio between the primaries, we analyze the interplay between collision orbits and various final motions and construct several types of dynamics. In particular, we show that orbits corresponding to any combination of past and future final motions can be created to pass arbitrarily close to the massive primary. Additionally, we construct arbitrarily large ejection-collision orbits (orbits which experience collision in both past and future times) and periodic orbits that are arbitrarily large and get arbitrarily close to the massive primary. Furthermore, we also establish oscillatory motions in both position and velocity, meaning that as time tends to infinity, the superior limit of the position or velocity is infinity while the inferior limit remains a real number.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809138","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":"A Generalization of Cardy’s and Schramm’s Formulae","authors":"Mikhail Khristoforov,&nbsp;Mikhail Skopenkov,&nbsp;Stanislav Smirnov","doi":"10.1007/s00220-025-05255-z","DOIUrl":"10.1007/s00220-025-05255-z","url":null,"abstract":"<div><p>We study critical site percolation on the triangular lattice. We find the difference of the probabilities of having a percolation interface to the right and to the left of two given points (such that the union of the triangles intersecting the interface does not separate the points) in the scaling limit. This generalizes both Cardy’s and Schramm’s formulae. The generalization involves a new interesting discrete analytic observable and an unexpected conformal mapping.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05255-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809139","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":"Operator-Valued Twisted Araki–Woods Algebras","authors":"R. Rahul Kumar,&nbsp;Melchior Wirth","doi":"10.1007/s00220-025-05285-7","DOIUrl":"10.1007/s00220-025-05285-7","url":null,"abstract":"<div><p>We introduce operator-valued twisted Araki–Woods algebras. These are operator-valued versions of a class of second quantization algebras that includes <i>q</i>-Gaussian and <i>q</i>-Araki–Woods algebras and also generalize Shlyakhtenko’s von Neumann algebras generated by operator-valued semicircular variables. We develop a disintegration theory that reduces the isomorphism type of operator-valued twisted Araki–Woods algebras over type <span>(textrm{I})</span> factors to the scalar-valued case. Moreover, these algebras come with a natural weight, and we characterize its modular theory. We also give sufficient criteria that guarantee the factoriality of these algebras.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05285-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809140","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":"Delocalisation and Continuity in 2D: Loop (textrm{O}(2)), Six-Vertex, and Random-Cluster Models","authors":"Alexander Glazman,&nbsp;Piet Lammers","doi":"10.1007/s00220-025-05259-9","DOIUrl":"10.1007/s00220-025-05259-9","url":null,"abstract":"<div><p>We prove the existence of macroscopic loops in the loop <span>(textrm{O}(2))</span> model with <span>(frac{1}{2}le x^2le 1)</span> or, equivalently, delocalisation of the associated integer-valued Lipschitz function on the triangular lattice. This settles one side of the conjecture of Fan, Domany, and Nienhuis (1970 s–1980 s) that <span>(x^2 = frac{1}{2})</span> is the critical point. We also prove delocalisation in the six-vertex model with <span>(0&lt;a,,ble cle a+b)</span>. This yields a new proof of continuity of the phase transition in the random-cluster and Potts models in two dimensions for <span>(1le qle 4)</span> relying neither on integrability tools (parafermionic observables, Bethe Ansatz), nor on the Russo–Seymour–Welsh theory. Our approach goes through a novel FKG property required for the non-coexistence theorem of Zhang and Sheffield, which is used to prove delocalisation all the way up to the critical point. We also use the <span>({mathbb {T}})</span>-circuit argument in the case of the six-vertex model. Finally, we extend an existing renormalisation inequality in order to quantify the delocalisation as being logarithmic, in the regimes <span>(frac{1}{2}le x^2le 1)</span> and <span>(a=ble cle a+b)</span>. This is consistent with the conjecture that the scaling limit is the Gaussian free field.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05259-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809141","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":"Contact Discontinuities for 2-D Isentropic Euler are Unique in 1-D but Wildly Non-unique Otherwise","authors":"Sam G. Krupa,&nbsp;László Székelyhidi Jr.","doi":"10.1007/s00220-025-05278-6","DOIUrl":"10.1007/s00220-025-05278-6","url":null,"abstract":"<div><p>We develop a general framework for studying non-uniqueness of the Riemann problem for the isentropic compressible Euler system in two spatial dimensions, and in this paper we present the most delicate result of our method: non-uniqueness of the contact discontinuity. Our approach is computational, and uses the pressure law as an additional degree of freedom. The stability of the contact discontinuities for this system is a major open problem (see Chen and Wang, in: Nonlinear partial differential equations, Abel Symposia, vol 7, Springer, Heidelberg, 2012). We find a smooth pressure law <i>p</i>, verifying the physically relevant condition <span>(p'&gt;0)</span>, such that for the isentropic compressible Euler system with this pressure law, contact discontinuity initial data is wildly non-unique in the class of bounded, admissible weak solutions. This result resolves the question of uniqueness for contact discontinuity solutions in the compressible regime. Moreover, in the <i>same regularity class</i> in which we have non-uniqueness of the contact discontinuity, i.e. <span>(L^infty )</span>, with no <i>BV</i> regularity or self-similarity, we show that the classical contact discontinuity solution to the two-dimensional isentropic compressible Euler system is in fact <i>unique</i> in the class of bounded, admissible weak solutions if we restrict to 1-D solutions.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809368","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":"Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus","authors":"Igor Burban,&nbsp;Semyon Klevtsov","doi":"10.1007/s00220-025-05267-9","DOIUrl":"10.1007/s00220-025-05267-9","url":null,"abstract":"<div><p>In 1993 Keski-Vakkuri and Wen introduced a model for the fractional quantum Hall effect based on multilayer two-dimensional electron systems satisfying quasi-periodic boundary conditions. Such a model is essentially specified by a choice of a complex torus <i>E</i> and a symmetric positively definite matrix <i>K</i> of size <i>g</i> with non-negative integral coefficients, satisfying some further constraints. The space of the corresponding wave functions turns out to be <span>(delta )</span>-dimensional, where <span>(delta )</span> is the determinant of <i>K</i>. We construct a hermitian holomorphic bundle of rank <span>(delta )</span> on the abelian variety <i>A</i> (which is the <i>g</i>-fold product of the torus <i>E</i> with itself), whose fibres can be identified with the space of wave function of Keski-Vakkuri and Wen. A rigorous construction of this “magnetic bundle” involves the technique of Fourier–Mukai transforms on abelian varieties. The constructed bundle turns out to be simple and semi-homogeneous and it can be equipped with two different (and natural) hermitian metrics: the one coming from the center-of-mass dynamics and the one coming from the Hilbert space of the underlying many-body system. We prove that the canonical Bott–Chern connection of the first hermitian metric is always projectively flat and give sufficient conditions for this property for the second hermitian metric.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05267-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769778","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":"The q-Immanants and Higher Quantum Capelli Identities","authors":"Naihuan Jing,&nbsp;Ming Liu,&nbsp;Alexander Molev","doi":"10.1007/s00220-025-05273-x","DOIUrl":"10.1007/s00220-025-05273-x","url":null,"abstract":"<div><p>We construct polynomials <span>(mathbb {S}_{mu }(z))</span> parameterized by Young diagrams <span>(mu )</span>, whose coefficients are central elements of the quantized enveloping algebra <span>(textrm{U}_q(mathfrak {gl}_n))</span>. Their constant terms coincide with the central elements provided by the general construction of Drinfeld and Reshetikhin. For another special value of <i>z</i>, we get <i>q</i>-analogues of Okounkov’s quantum immanants for <span>(mathfrak {gl}_n)</span>. We show that the Harish-Chandra image of <span>(mathbb {S}_{mu }(z))</span> is a factorial Schur polynomial. We derive quantum analogues of the higher Capelli identities by calculating the images of the <i>q</i>-immanants in the braided Weyl algebra. We also give a symmetric function interpretation and new proof of the Newton identities of Gurevich, Pyatov and Saponov.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05273-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769788","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":"Tensor K-Matrices for Quantum Symmetric Pairs","authors":"Andrea Appel,&nbsp;Bart Vlaar","doi":"10.1007/s00220-025-05241-5","DOIUrl":"10.1007/s00220-025-05241-5","url":null,"abstract":"<div><p>Let <span>({{mathfrak {g}}})</span> be a symmetrizable Kac–Moody algebra, <span>(U_q({{mathfrak {g}}}))</span> its quantum group, and <span>(U_q({mathfrak {k}})subset U_q({{mathfrak {g}}}))</span> a quantum symmetric pair subalgebra determined by a Lie algebra automorphism <span>(theta )</span>. We introduce a category <span>(mathcal {W}_{theta })</span> of <i>weight</i> <span>(U_q({mathfrak {k}}))</span>-modules, which is acted on by the category of weight <span>(U_q({{mathfrak {g}}}))</span>-modules via tensor products. We construct a universal tensor K-matrix <span>({{mathbb {K}}} )</span> (that is, a solution of a reflection equation) in a completion of <span>(U_q({mathfrak {k}})otimes U_q({{mathfrak {g}}}))</span>. This yields a natural operator on any tensor product <span>(Motimes V)</span>, where <span>(Min mathcal {W}_{theta })</span> and <span>(Vin {{mathcal {O}}}_theta )</span>, <i>i.e.</i>, <i>V</i> is a <span>(U_q({{mathfrak {g}}}))</span>-module in category <span>({{mathcal {O}}})</span> satisfying an integrability property determined by <span>(theta )</span>. Canonically, <span>(mathcal {W}_{theta })</span> is equipped with a structure of a bimodule category over <span>({{mathcal {O}}}_theta )</span> and the action of <span>({{mathbb {K}}} )</span> is encoded by a new categorical structure, which we call a <i>boundary</i> structure on <span>(mathcal {W}_{theta })</span>. This generalizes a result of Kolb which describes a braided module structure on finite-dimensional <span>(U_q({mathfrak {k}}))</span>-modules when <span>({{mathfrak {g}}})</span> is finite-dimensional. We also consider our construction in the case of the category <span>({{mathcal {C}}})</span> of finite-dimensional modules of a quantum affine algebra, providing the most comprehensive universal framework to date for large families of solutions of parameter-dependent reflection equations. In this case the tensor K-matrix gives rise to a formal Laurent series with a well-defined action on tensor products of any module in <span>(mathcal {W}_{theta })</span> and any module in <span>({{mathcal {C}}})</span>. This series can be normalized to an operator-valued rational function, which we call trigonometric tensor K-matrix, if both factors in the tensor product are in <span>({{mathcal {C}}})</span>.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05241-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769791","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}