GEWU Magazine

Restricted solid-on-solid (RSOS) model3 questions

Completing the lattice-to-continuum correspondence for integrable seams in unitary and nonunitary A-D-E minimal models: r-type seams, noncommutative $D_{2\ell}$ fusion algebras, and nonunitary dilogarithm identities
Sublinear variance bounds and the fluctuation order of the continuous-time restricted solid-on-solid (RSOS) surface growth model
Open problems in the factorization of reduced density matrices of the critical RSOS models: topological sectors, four-site decomposition, massive regimes, and rigorous foundations

Rogers–Ramanujan identities2 questions

Root-of-unity structure2 questions

RTT relation3 questions

Scaling Potts model2 questions

Sine-Gordon model4 questions

Sklyanin algebra4 questions

Slavnov-type scalar product1 questions

Complete spectrum and Slavnov-type scalar products for the open XYZ spin-1/2 chain beyond the linear boundary constraint
Open for about 38 years

SOS height variables4 questions

Square Lattice Eight-Vertex Model7 questions

Square-Lattice Ising Model5 questions

STM single-atom/molecule manipulation and applications in nanotechnology6 questions

stochastic vertex models3 questions

TBA and the

Y

-system3 questions

Temperley–Lieb algebra2 questions

tensor network renormalization（TNR）2 questions

tensor renormalization group（TRG）2 questions

The Mean Field Model7 questions

The One-dimensional Ising Model1 questions

Dynamic phase transition in the periodically driven one-dimensional Ising chain: existence, the dimensional mechanism, and the stationarity scaling
Open for about 11 years

The Spherical Model6 questions

thermodynamic Bethe Ansatz（TBA）4 questions

Theta functions4 questions

Theta function algebraic identities1 questions

Liu's $q\to1$ degeneration conjecture: reduction of the $\chi_5$ theta-function identity (3.80) to the cyclotomic-unit logarithm

Theta function series expansion2 questions

Tracy–Widom distribution1 questions

Divisibility and decomposability structure of the Tracy–Widom laws: free infinite divisibility, the GSE and β-Hermite finite-N cases, indecomposability, and divisible interpolation families

transfer-matrix fixed point1 questions

Chaotic RG flows and aperiodic critical times in the exact transfer-matrix renormalization group of the quench-driven Q-state clock chain

Tutte Polynomial2 questions

twisted boundary condition4 questions

ultraviolet CFT limit3 questions

universal

R

-matrix4 questions

van der Waals Fluid and Classical Critical Exponents2 questions

Virasoro Minimal Model4 questions

Wronskian Relations2 questions

XYZ Chain Spectrum3 questions

Yang Spontaneous Magnetization2 questions

Yang–Baxter Equation2 questions

Completing the lattice-to-continuum correspondence for integrable seams in unitary and nonunitary A-D-E minimal models: r-type seams, noncommutative D2ℓD_{2\ell}D2ℓ​ fusion algebras, and nonunitary dilogarithm identities

Sublinear variance bounds and the fluctuation order of the continuous-time restricted solid-on-solid (RSOS) surface growth model

Open problems in the factorization of reduced density matrices of the critical RSOS models: topological sectors, four-site decomposition, massive regimes, and rigorous foundations

Nahm's problem: classify the rational triples (A, B, C) for which the Nahm sum fA,B,C(q)f_{A,B,C}(q)fA,B,C​(q) is a modular function

Explicit tableau-pair families for the Rogers–Ramanujan summands and the direct Rogers–Ramanujan bijection (Stanton's Problem 2.3, with the row-restricted Cauchy Speculation 4.2)

Completing the categorical Temperley-Lieb framework: weakened rigidity for ModTL\mathrm{Mod}_{\mathrm{TL}}ModTL​ at roots of unity, the dilute commutor versus integrable 19-vertex weights, and fusion with braiding for the blob and affine families

Rigorous passage from the Jones quotients of the Temperley-Lieb algebras to the Virasoro minimal unitary models

Structural completion of the deformed (braided) gl(2|2) Yangian: the Yangian double, quantum determinant and center, crossing monodromy, and the secret-symmetry tower

Identifying the qqq-Pochhammer, Dickson, and Bessel algebras of the orthogonalization of Yangians

Completeness of the nested Bethe ansatz for the RTT algebra of sp(4) type (extended Yangian of sp(4))

Exchange-versus-bootstrap S-matrix crossover in the near-critical three-state quantum Potts chain: the scale p* and its dangerously irrelevant origin

Universal critical-amplitude ratios of the two-dimensional four-state Potts universality class: settling the two-kink form-factor versus Monte Carlo/series discrepancy

Full construction of the subcritical sine-Gordon Euclidean field theory: all couplings λ∈R\lambda\in\mathbb{R}λ∈R and β2<8π\beta^{2}<8\piβ2<8π in infinite volume, massive and massless

Charge-conjugation-odd conserved quantities underlying ballistic topological-charge transport in the sine-Gordon model

Renormalised higher-spin conserved currents of the massless sine-Gordon model: correlation functions, convergence, and quantum corrections

Form factors of the U(1) composite branch-point twist field in the soliton-antisoliton sector of the sine-Gordon model

Isomorphism classification of three-generator Sklyanin algebras over fields of characteristic 3 and over fields without a nontrivial cubic root of unity

Direct continuum quantization of the anisotropic Landau–Lifshitz model and the continuum origin of the Sklyanin algebra

Zariski cancellation for Sklyanin algebras of dimension at least three (the PI and four-dimensional cases)

Maximal level of a good specialization and explicit forms of the dimension-sss irreducible representations of a PI 4-dimensional Sklyanin algebra

Complete spectrum and Slavnov-type scalar products for the open XYZ spin-1/2 chain beyond the linear boundary constraint

The scaling limit of the integer-valued solid-on-solid model in the rough phase

Thermodynamic limit of the elliptic SOS model with domain-wall boundaries at general anisotropy, and its connection to the three-colouring functional equations

Layering transitions, exact wetting point, and critical behavior of the two-dimensional Solid-on-Solid wetting model beyond the low-temperature regime

Macroscopic shape of the (2+1)-dimensional solid-on-solid surface with wall pinning in the delocalized phase: two-level concentration, pinning-dependent height shift, and level-line scaling limits

Symmetry algebra underlying the transfer-matrix degeneracies of the eight-vertex model at elliptic roots of unity

Analytic foundations of the new Q-matrix for the eight-vertex model at roots of unity: regularity, functional relations, and the t≠0t\neq 0t=0 similarity structure

Rigorous fluctuation theory for the stochastic eight-vertex model: Boltzmann–Gibbs replacement principles, the two-noise KPZ–Burgers limit SPDE, and classification of translation-invariant invariant measures

Conjecture 5.1 of Hagendorf and Liénardy: an eigenvalue formula for the inhomogeneous supersymmetric eight-vertex model on a strip

Critical behavior of the eight-vertex model in electric fields beyond the c=dc=dc=d subspace: robustness of weak universality and the electric critical exponents

Finite-lattice integrability of the free-fermion odd eight-vertex model: commuting transfer matrices for the asymmetric and staggered cases

Form factors of local operators and correlation functions of the inhomogeneous eight-vertex (XYZ) model via the generalized algebraic Bethe ansatz

Coexistence of infinite +++ and −-− clusters in the Ising model on the square matching lattice Z∗2\mathbb{Z}_*^2Z∗2​ for all subcritical temperatures

Continuity, critical-current geometry, and Pfaffian universality for two-dimensional finite-range Ising models

Differential-equation characterization of the leading finite-size corrections to the two-dimensional Ising two-point scaling function in general lattice position

Existence of a nonlinear Painlevé-type ordinary differential equation for the row correlation functions of the two-dimensional Ising model

Fisher-zero accumulation geometry and free-energy analyticity of the square-lattice Ising model at generic nonzero magnetic field

Generalization, tip-change robustness, and physical interpretation of deep-reinforcement-learning control in autonomous atom manipulation

Real-time dynamics, interfacial-charge mechanism, and directionality control of electrostatically driven long-distance single-molecule motion on surfaces

Saturation capacity, atomic-scale structure, method generality, and catalytic/magnetic properties of atom-by-atom assembled clusters in Si(111)-(7×7) half-unit cells by mechanical gating

Closing the autonomy and inverse-design loop for atom-by-atom fabrication of artificial lattices with designer electronic states

Gate-controlled reconfiguration and coherent dynamics of atom-assembled quantum-dot molecules on InAs(111)A

Verified atomic identity, transfer to Si(001), and encapsulation of phosphorus implanted into silicon by STM-tip manipulation of P4P_4P4​

Interpolation between the stochastic telegraph equation and KPZ fluctuation limits of the stochastic six-vertex model

Half-space symmetry classification for the colored stochastic six-vertex model: Galashin-type characterization and shift invariance for height functions not crossing the diagonal

Exact non-equilibrium steady state of the boundary-driven multispecies harmonic process: factorised form and mixture representation

Equivalence between the decoupled sine-Gordon thermodynamic Bethe Ansatz system and the conjectured sine-Gordon Y-system

Open analytic problems in the thermodynamics of Inozemtsev's elliptic spin chain: string classification, supersymmetric equivalence, and reduction of the elliptic Y-system

Non-principal ('snake') YYY-systems and exact finite-size corrections for the twisted A2(1)A_2^{(1)}A2(1)​ and A2(2)A_2^{(2)}A2(2)​ lattice models

Iterated binary fusion versus single m-fold fusion for families of modules over the enlarged periodic Temperley–Lieb algebra

Completing the exact solution of the Uqsl2U_q\mathfrak{sl}_2Uq​sl2​-invariant non-compact boundary XXZ chain: two-boundary Temperley–Lieb representation theory at roots of unity, indecomposable boundary weights, critical scaling limits, and fusion

Open problems of the Newton-with-rotation method for critical tensor network renormalization group fixed points (Ebel–Kennedy–Rychkov)

Defect-preserving tensor-network coarse graining and the smearing-radius growth law at criticality

Large-NNN volume independence in the tensor renormalization group beyond two-dimensional pure gauge: self-similar singular-value spectra in d≥3d\ge 3d≥3 and O(1)O(1)O(1) topological volume independence with matter fields

Predictive theory of bond-dimension convergence and truncation-induced length scales in plain tensor renormalization group

Clustering transition and Bethe-state decomposition for Gibbs measures on sparse random graphs

Finite-NNN crossover from Vlasov to Boltzmann-Gibbs critical behavior in the Hamiltonian mean-field model

Global complex-temperature phase diagram of the Curie–Weiss model: the critical curve conjecture of Shamis and Zeitouni

Extending force-monopole micromechanics of a mean-field glass model to sparse connectivity, mesoscopic-elasticity/boson-peak predictions, and driven dynamics

Vlasov response, fluctuation-dissipation, and collective 1/f fluctuations in mean-field classical Heisenberg spin systems beyond second-order transitions

Nuclear spectral theory for the Ruelle–Araki transfer operator beyond exponential decay: one-dimensional interactions with polynomial and stretched-exponential tails

Finite-γ spontaneous magnetization of the layered Kac Ising model at the mean-field critical temperature and its convergence to the Lebowitz–Penrose phase diagram

Dynamic phase transition in the periodically driven one-dimensional Ising chain: existence, the dimensional mechanism, and the stationarity scaling

Out-of-equilibrium dynamics and thermodynamics of the active spherical model

Hierarchical O(N)O(N)O(N) Heisenberg-to-spherical convergence in the local potential approximation and the 1/N1/N1/N viscosity expansion of the renormalization-group PDE

Onset of nonconcavity and ensemble nonequivalence in the microcanonical entropy of the spherical model as the interaction range is varied, and genericity of two-transition microcanonical phase diagrams for short-range ferromagnets

Robustness of momentum-interaction-induced re-entrant quantum criticality beyond the exactly solved spin-anisotropic quantum spherical model

Exact finite-size scaling of the three-dimensional mean spherical model with Neumann–Dirichlet boundary conditions and surface fields in the regime at and below the film critical point

Demagnetization artifact and ternary extensions in exactly solvable multicomponent spherical models of fluid criticality

Well-posedness of the generalized thermodynamic Bethe ansatz beyond the repulsive Lieb-Liniger model: string, nested and attractive structures, and non-polynomial driving functions

Global solution of the infinite thermodynamic Bethe-ansatz string hierarchy of the one-dimensional attractive Hubbard model

Thermodynamic Bethe Ansatz completeness for the surface free energy of the open XXZ spin-1/2 chain

Analytic foundations of the Thermodynamic Bethe Ansatz solution to the Donaldson-Thomas Riemann-Hilbert problem of the A2 quiver (deformed cubic oscillator)

Rigorous analytic status of the theta-function Zamolodchikov-algebra constructions for the Belavin model: the NNN-dependence of the case-2 alternative algebra

Exact grand partition functions, modularity, and quantization conditions for the orientifold ABJ Fermi gas at general Chern-Simons level kkk

Exact solution of the elliptic and hyperbolic near-neighbors Jastrow models beyond the ground state: excited eigenfunctions, spin generalizations, and correlation functions

Theta-function solution space of the level-one elliptic qKZB equation: wheel-condition classification and the first-excited-state conjecture in the three-colour model

Liu's q→1q\to1q→1 degeneration conjecture: reduction of the χ5\chi_5χ5​ theta-function identity (3.80) to the cyclotomic-unit logarithm

Liu's Conjecture 3.10: the q→1q\to1q→1 degeneration of a degree-eight theta-function identity to a quadratic-character logarithmic series

Open problems on the Rogers–Ramanujan dissection of a theta function: multi-factor dissections, an sss-parameter companion family, physical interpretation, and partition-theoretic content

Completing the lattice-to-continuum correspondence for integrable seams in unitary and nonunitary A-D-E minimal models: r-type seams, noncommutative $D_{2\ell}$ fusion algebras, and nonunitary dilogarithm identities

Nahm's problem: classify the rational triples (A, B, C) for which the Nahm sum $f_{A,B,C}(q)$ is a modular function

Completing the categorical Temperley-Lieb framework: weakened rigidity for $\mathrm{Mod}_{\mathrm{TL}}$ at roots of unity, the dilute commutor versus integrable 19-vertex weights, and fusion with braiding for the blob and affine families

Identifying the $q$ -Pochhammer, Dickson, and Bessel algebras of the orthogonalization of Yangians

Full construction of the subcritical sine-Gordon Euclidean field theory: all couplings $\lambda\in\mathbb{R}$ and $\beta^{2}<8\pi$ in infinite volume, massive and massless

Maximal level of a good specialization and explicit forms of the dimension- $s$ irreducible representations of a PI 4-dimensional Sklyanin algebra

Analytic foundations of the new Q-matrix for the eight-vertex model at roots of unity: regularity, functional relations, and the $t\neq 0$ similarity structure

Critical behavior of the eight-vertex model in electric fields beyond the $c=d$ subspace: robustness of weak universality and the electric critical exponents

Coexistence of infinite $+$ and $-$ clusters in the Ising model on the square matching lattice $\mathbb{Z}_*^2$ for all subcritical temperatures

Verified atomic identity, transfer to Si(001), and encapsulation of phosphorus implanted into silicon by STM-tip manipulation of $P_4$

Non-principal ('snake') $Y$ -systems and exact finite-size corrections for the twisted $A_2^{(1)}$ and $A_2^{(2)}$ lattice models

Completing the exact solution of the $U_q\mathfrak{sl}_2$ -invariant non-compact boundary XXZ chain: two-boundary Temperley–Lieb representation theory at roots of unity, indecomposable boundary weights, critical scaling limits, and fusion

Large- $N$ volume independence in the tensor renormalization group beyond two-dimensional pure gauge: self-similar singular-value spectra in $d\ge 3$ and $O(1)$ topological volume independence with matter fields

Finite- $N$ crossover from Vlasov to Boltzmann-Gibbs critical behavior in the Hamiltonian mean-field model

Hierarchical $O(N)$ Heisenberg-to-spherical convergence in the local potential approximation and the $1/N$ viscosity expansion of the renormalization-group PDE

Rigorous analytic status of the theta-function Zamolodchikov-algebra constructions for the Belavin model: the $N$ -dependence of the case-2 alternative algebra

Exact grand partition functions, modularity, and quantization conditions for the orientifold ABJ Fermi gas at general Chern-Simons level $k$

Liu's $q\to1$ degeneration conjecture: reduction of the $\chi_5$ theta-function identity (3.80) to the cyclotomic-unit logarithm

Liu's Conjecture 3.10: the $q\to1$ degeneration of a degree-eight theta-function identity to a quadratic-character logarithmic series

Open problems on the Rogers–Ramanujan dissection of a theta function: multi-factor dissections, an $s$ -parameter companion family, physical interpretation, and partition-theoretic content

Completing the approximability classification of the parameterized Tutte polynomial at rational points with $(x-1)(y-1)\notin[0,1]$

Closure of the quantum separation-of-variables program for twisted $gl_{\mathcal{M}|\mathcal{N}}$ spin chains and the inhomogeneous Hubbard model

Classification, Hamiltonian structure, and quantum S-matrices of $\mathbb{Z}_N$ -twisted trigonometric sigma models

Universal $R$ -matrix of the double-parameter quantum affine superalgebra of type $A(0,2)^{(4)}$