We study the spatial overlap of successive spin configurations generated by Markov chain Monte Carlo simulations of the Baxter–Wu model. Using the Novotny–Evertz sublattice-freezing single-cluster update, we track the mean and variance of the algorithmic overlap across the critical region. We show that, even in this three-spin model, the overlap acts as an algorithmic observable that follows the thermodynamics of the transition: the single-cluster overlap mean behaves like an order parameter, dropping from a finite ordered-phase plateau toward zero across <italic>T<inf>c</inf></italic>. The overlap does not diverge at criticality, instead it remains finite and its finite-size value decays as a clean power law, <math altimg='si29.svg'><mrow><msub><mi>U</mi><mn>2</mn></msub><mrow><mo>(</mo><msub><mi>T</mi><mi>c</mi></msub><mo>)</mo></mrow><mo>&#8764;</mo><msup><mi>L</mi><mrow><mo>&#8722;</mo><mi>&#968;</mi></mrow></msup></mrow></math>, over eleven sizes with an exponent <math altimg='si30.svg'><mrow><mi>&#968;</mi><mo linebreak='goodbreak'>=</mo><mn>0.378</mn><mo>(</mo><mn>4</mn><mo>)</mo></mrow></math>. The exponent is stable under removal of small and large sizes and under the correction-to-scaling terms known for this model, which enter with amplitudes consistent with zero. It differs by more than eight standard errors from the values found for the Ising, three-state Potts and four-state Potts models under standard Fortuin&#8211;Kasteleyn Wolff dynamics. The Novotny&#8211;Evertz clusters reproduce the susceptibility exponent <math altimg='si21.svg'><mrow><mi>&#947;</mi><mo linebreak='goodbreak'>/</mo><mi>&#957;</mi><mo linebreak='goodbreak'>=</mo><mn>7</mn><mo linebreak='goodbreak'>/</mo><mn>4</mn></mrow></math>, which the Ising model shares, so the difference is not set by the static exponents or by the cluster-size exponent.

Russia

Ian Pilé

Lev Shchur

Algorithmic overlaps in the Baxter–Wu model: Cluster dynamics under Novotny–Evertz updates

In this article, we provide a detailed characterization of the optical properties of the metamaterial associated with Schwarzschild space in the presence of a cosmological constant, using the analogy between spacetime and anisotropic metamaterials. The scalar construction is a trajectory-specific inverse-designed GRIN model, engineered per ray, so that its agreement with the geodesics verifies the numerical implementation rather than establishing an independent spacetime–medium correspondence; the tensorial Plebański medium, by contrast, is fixed by the metric alone. We explicitly show the refractive index associated with the metamaterial and find that the cosmological constant provides interesting optical properties to the metamaterial. For Λ > 0 we show that the cosmological term displaces the critical impact parameter to <math altimg='si77.svg'><mrow><msub><mi>b</mi><mi>c</mi></msub><mo linebreak='goodbreak'>=</mo><mn>3</mn><msqrt><mn>3</mn></msqrt><mi>M</mi><mo linebreak='goodbreak'>/</mo><msqrt><mrow><mn>1</mn><mo linebreak='badbreak'>&#8722;</mo><mn>9</mn><msup><mi>M</mi><mn>2</mn></msup><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle></mrow></msqrt></mrow></math> while leaving the photon sphere at <math altimg='si78.svg'><mrow><mi>r</mi><mo linebreak='goodbreak'>=</mo><mn>3</mn><mi>M</mi></mrow></math>, so that rays which are marginally supercritical in the asymptotically flat case are captured. We further prove that the Rindler&#8211;Ishak correction factor coincides with the local anisotropy ratio <math altimg='si79.svg'><mrow><msub><mi>n</mi><mi>&#981;</mi></msub><mo linebreak='goodbreak'>/</mo><msub><mi>n</mi><mi>r</mi></msub><mo linebreak='goodbreak'>=</mo><msqrt><mi>f</mi></msqrt></mrow></math> of the Pleba&#324;ski medium, and that this identifies the effect with the splitting between the ray and wave-normal directions that any anisotropic medium produces: the Rindler&#8211;Ishak angle is the geometric mean of the two, <math altimg='si80.svg'><mrow><mi>tan</mi><msub><mi>&#968;</mi><mrow><mrow><mi mathvariant='normal'>i</mi></mrow><mi>n</mi><mi>v</mi></mrow></msub><mo linebreak='goodbreak'>=</mo><msqrt><mrow><mi>tan</mi><msub><mi>&#968;</mi><mrow><mrow><mi mathvariant='normal'>r</mi></mrow><mi>a</mi><mi>y</mi></mrow></msub><mi>tan</mi><msub><mi>&#952;</mi><mi>k</mi></msub></mrow></msqrt></mrow></math>, and both angles are separately measurable in the analogue system. Fixing the emission condition in the measured rather than the coordinate sense, we find that a positive cosmological term <italic>suppresses</italic> the deflection recorded between a static emitter and receiver at finite radius, by 80% at the value used here, so that what it enhances is the capture window and not the bending. Conversely, for &#923;&#8239;&lt;&#8239;0 the absence of a global Euclidean embedding translates into an imaginary scalar index acting as an algebraic censor, while the exact tensorial mapping yields a matched uniaxial zero-index medium ( <math altimg='si81.svg'><mrow><msub><mi>&#955;</mi><mi>&#981;</mi></msub><mo linebreak='goodbreak'>=</mo><msub><mi>&#955;</mi><mi>z</mi></msub><mo>&#8594;</mo><mn>0</mn></mrow></math>, <math altimg='si82.svg'><mrow><msub><mi>&#955;</mi><mi>r</mi></msub><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math>, <math altimg='si20.svg'><mrow><mi>Z</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math>) whose radial constitutive component remains that of vacuum. The two causal boundaries unify into a single optical statement: de Sitter has infinite optical thickness at finite radius, Anti-de Sitter finite optical thickness at infinite radius.

Mexico

M.A. García-Sánchez

J.L. López-Picón

E.A. Mena-Barboza

Anisotropic metamaterials analogue to non-asymptotically flat spacetime geometries

<list id='lst0001'><list-item id='lstitem0001'><label>&#8226;</label><para id='p0001'>Exact plane-wave solutions of SU(2) Yang-Mills equations: complete classification.</para></list-item><list-item id='lstitem0002'><label>&#8226;</label><para id='p0002'>Genuinely non-Abelian waves require <italic>&#946;</italic>&#8239;&#215;&#8239;&#8467;&#8239;&#8800;&#8239;0 and contain a nonlinear second harmonic.</para></list-item><list-item id='lstitem0003'><label>&#8226;</label><para id='p0003'>Zero-action family links vacuum to non-Abelian waves; energy grows nonlinearly.</para></list-item></list>

China

Yu-Xuan Zhang

Jing-Ling Chen

A genuinely non-Abelian plane-wave solution of the SU(2) Yang-Mills equations

Two regular black hole cores are covered by the same exponentially localized anisotropic sector. A Bardeen seed with positive mass produces a de Sitter core, whereas an exponential hollow seed produces a Minkowski core. The comparison examines how adding or redistributing the finite mass carried by the hair changes horizons and capture from infinity. Holding the seed mass or the Arnowitt–Deser–Misner mass fixed defines different paths through the same family. Joint diagrams in seed mass and hair amplitude resolve regions with four horizons, cusp configurations, and two simultaneous double horizons. The analysis also compares rotating extensions of the Kerr geometry. Exchanging two accessible photon barriers of equal height preserves the critical impact parameter. A new outer horizon can instead hide the dominant barrier and produce a finite jump, even at fixed total mass. A sufficient bound establishes the static exterior weak energy condition for all positive seed masses at the studied ratios of core length to hair length. An explicit static magnetic action realizes the horizon differential as a covariant law with varying couplings and exhibits a failure of a necessary exterior propagation condition. Exterior approaches to the ring exclude a <italic>C</italic> <sup>1</sup> Bardeen or <italic>C</italic> <sup>2</sup> hollow extension with hair in the usual Cartesian Kerr&#8211;Schild smooth structure. The hairless hollow boundary admits a locally smooth disk completion. The results connect mass redistribution to horizon structure and capture, with explicit tests of the matter dynamics and rotating geometry.

Kazakhstan

Daulet Berkimbayev

Regular hairy black holes by gravitational decoupling: De Sitter and Minkowski cores

In this paper, we relate the Macdonald index of a 4d <math altimg='si17.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math> <sans-serif>SCFT</sans-serif> with the Hilbert series of the arc space of the Zhu&#8217;s <italic>C</italic> <inf>2</inf>-algebra of the corresponding Schur <sans-serif>VOA</sans-serif>. Using this, we conjecture a simple formula for the Macdonald index of <math altimg='si18.svg'><mrow><mo>(</mo><msub><mi>A</mi><mn>1</mn></msub><mo>,</mo><msub><mi>D</mi><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>)</mo></mrow></math> Argyres-Douglas theory. We perform checks of the formula against the known Schur limits and <sans-serif>RG</sans-serif> flows. To match the Schur limit, we prove new <italic>q</italic>-series identities.

United States

George Andrews

Anindya Banerjee

United Kingdom

Chinmaya Bhargava

Ranveer Kumar Singh

Runkai Tao

Argyres-Douglas theories, Macdonald indices and the arc space of Zhu’s <italic>C</italic> <inf>2</inf>-algebra

In this paper, we investigate a fractional three-component modified Korteweg-de Vries (mKdV) equation by introducing the Riesz fractional derivative and employing the completeness relations of the squared eigenfunctions and their adjoint counterparts. Subsequently, a Riemann-Hilbert problem is formulated, from which exact fractional N-soliton solutions are derived in determinant form under the reflectionless condition. Representative examples of fractional one- and two-soliton solutions demonstrate that the fractional-order parameter has a significant influence on soliton peak positions and propagation displacements.

Lin Sun

Ziyuan Liu

Huihui Pang

Yuqin Yao

Azerbaijan

South Africa

Wen-Xiu Ma

The Riemann-Hilbert method for an integrable fractional three-component modified Korteweg-de Vries equation

The IDEA (Innovative Detector for Electron-positron Accelerator) drift chamber is a large, ultra-light gaseous tracking detector whose very low material budget is enabled by an innovative wire-support and assembly concept. Its large dimensions, combined with the requirements of low mass and high stiffness, pose significant challenges for structural design and material selection. This work presents a preliminary structural design of the wire cage, with particular emphasis on the endplates, which consist of an outer ring, an inner ring, radial spokes, and suspension cables supporting almost 340,000 anodic and cathodic wires. A hierarchical two-stage optimization strategy is adopted. In the first stage, Response Surface Methodology and Kriging surrogate models are used for geometric sizing, seeking a compromise between low structural mass, reduced spoke deformation, and adequate buckling resistance. In the second stage, a genetic algorithm is used to optimize the suspension-cable prestresses and further reduce spoke deflection. The optimized prestress distribution reduces the maximum spoke deflection from 24.34 mm to 0.564 mm. Although this value remains above the preliminary working target of 0.2 mm, the results demonstrate the effectiveness and structural feasibility of the cable-stayed endplate concept at the present preliminary-design stage. Further refinement will be required once the final composite material system and detector-level requirements have been defined.

Italy

Mauro Corrado

Giorgio Zavarise

Rakesh Rawat

Francesco Grancagnolo

Preliminary structural design of the IDEA drift chamber

We study a <math altimg='si17.svg'><mrow><mo>(</mo><mn>3</mn><mo linebreak='goodbreak'>+</mo><mn>1</mn><mo>)</mo></mrow></math>-dimensional nonlinear evolution equation carrying a nonlocal term through the operator <math altimg='si18.svg'><msubsup><mi>&#8706;</mi><mi>x</mi><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msubsup></math>, and we build a single machine-learning framework that unifies forward solution learning, inverse coefficient discovery, and automatic solution certification. The central step is to let a neural network carry the Hirota bilinear <italic>&#964;</italic>-function rather than the physical field, to train it with the residual of the bilinear equation, and to recover the field through the exact logarithmic map <math altimg='si19.svg'><mrow><mi>&#968;</mi><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>3</mn><msub><mrow><mo>(</mo><mi>ln</mi><mi>G</mi><mo>)</mo></mrow><mrow><mi>x</mi><mi>x</mi></mrow></msub></mrow></math>. The bilinear equation obtained in this way is, up to sign, the bilinear form of the Jimbo&#8211;Miwa equation, so the model inherits the conditional integrability of that equation. This choice removes the nonlocal operator by construction, represents singular and complex waves directly, because singularities of the field are zeros of a smooth <italic>&#964;</italic>-function, and yields a differentiable functional that certifies whether any candidate closed form is a true solution. Using the certification analysis we revisit the exact solutions recently reported for this equation and prove, with symbolic derivations and high-precision numerical certificates, that the non-singular and singular complexiton families do not satisfy the equation and that the equation admits Hirota one- and two-soliton solutions but fails the three-soliton condition for generic wave numbers, the hierarchy surviving only on restricted parameter families. The corrected phase shift is supplied in closed form. The framework is validated on the true solutions, attains a relative error of about one percent on the forward problem, recovers the governing coefficients from noisy data, and continues to operate on a non-integrable perturbation for which no closed form exists.

Saudi Arabia

Mohammad Akram

Pakistan

Umar Ishtiaq

Romania

Ioan-Lucian Popa

Deep learning of Hirota <italic>&#964;</italic>-function for soliton solutions of a <math altimg='si17.svg'><mrow><mo>(</mo><mn>3</mn><mo linebreak='goodbreak'>+</mo><mn>1</mn><mo>)</mo></mrow></math>-dimensional nonlocal evolution equation

We present a gauge-theoretic formulation of Nambu non-equilibrium thermodynamics (NNET) within a common gauge-fixed worldline framework. In this formulation, the generalized thermodynamic force is described by an Abelian thermodynamic connection, and ordinary Onsager dynamics is recovered by fixing its temporal component through the dissipation function.

Japan

So Katagiri

A gauge-theoretic formulation of Nambu non-equilibrium thermodynamics

We study a four-dimensional <math altimg='si1.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math> supersymmetric Proca model with an explicit mass term for a real vector superfield and a generalized transverse kinetic operator. Although it displays no gauge redundancy in Proca variables, for local kinetic operators the model is the exact classical unitary-gauge form of the minimal Abelian <math altimg='si1.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math> Stueckelberg realization, with the SQED-like exponential as its minimal gauge-covariant matter coupling. We compute the K&#228;hlerian contribution to the one-loop effective action using both the background-field Hessian and an independent supergraph organization. In the minimal model the background-dependent divergence is local and is absorbed by the matter K&#228;hler normalization, and the finite local terms left by the subtraction remain scheme dependent. At <math altimg='si2.svg'><mrow><mi>&#945;</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>, an anomaly-free minimal Stueckelberg formulation supports a conditional perturbative-renormalizability interpretation for the corresponding minimal theory. For <math altimg='si3.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mo>&#9633;</mo><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mo>&#9633;</mo><mo>+</mo><mi>&#945;</mi><msup><mo>&#9633;</mo><mn>2</mn></msup></mrow></math> we distinguish the exact polynomial model, defined over the full momentum range, from a truncated derivative expansion; in the latter reading, the additional pole and the local matching term are ultraviolet information determined by the completion rather than predictions of the truncated theory.