GEWU Magazine

Two-body

S

matrix3 questions

Closed-form scattering of an arbitrary number of bound states and quantum integrability of the $O(2)_L\times O(2)_R$ chiral Gross–Neveu (Zakharov–Mikhailov) model
The intertwiner property for non-diagonal factorizing S-matrices in the operator-algebraic inverse scattering construction
Physical realization of the extremal 2D S-matrix $S=-S_{\mathrm{SG}}$ for a bound state with $m_1<\sqrt{2}\,m$ , and optimal coupling bounds away from integrable points

Toeplitz/Pfaffian correlation function structure of 2D Ising2 questions

Critical exponents of 2D Ising3 questions

2D Ising and Painlevé equations2 questions

2D Ising transfer matrix spectrum2 questions

Metal-insulator transition problem in two-dimensional electron systems at zero magnetic field8 questions

Zero-resistance phenomenon in two-dimensional electron systems under microwave irradiation6 questions

Conductivity minimum problem in two-dimensional graphite5 questions

Unsolved problem of 2D Ising in a general non-zero uniform magnetic field1 questions

Exact thermodynamics of the two-dimensional square-lattice Ising model in a uniform external magnetic field
Open for about 82 years

Two-spin and four-spin Ising representation1 questions

Rigorous analytic derivation of the electric critical exponents of the symmetric eight-vertex model ( $\eta_e = 1-\mu/\pi$ , $\delta_e = (3\pi+\mu)/(\pi-\mu)$ )

Antiferroelectric phase2 questions

Inversion relations1 questions

Completing the spectral theory of the degenerate chiral Potts models: eigenvectors and completeness, the $k'=0$ commuting Q-operator problem, and thermodynamics
Open for about 18 years

Instability mechanism of spiral waves in reaction-diffusion systems8 questions

Antiperiodic boundaries and interfacial tension2 questions

The square-lattice Ising model3 questions

The square-lattice Potts model1 questions

Completing the eigenvalue-amplitude theory of the Potts model on a torus: non-generic lattices, width-dependent level degeneracies, and the Beraha-number zero structure
Open for about 20 years

The square-lattice eight-vertex model3 questions

High–low temperature duality on the square lattice3 questions

The three-colouring problem on the square lattice4 questions

Affine Lie algebra characters4 questions

Non-difference-property model2 questions

Non-Born-Oppenheimer approximation problem6 questions

FFLO state of inhomogeneous Fermi superfluids2 questions

Nonequilibrium correlation function4 questions

Inhomogeneous eight-vertex model4 questions

Interface Effects of Nonlinear Wave Propagation8 questions

Nonlinear integral equation3 questions

Mathematical Model and Theory of Nonlinear Standing Wave Acoustic Fields6 questions

Is the Fibonacci double helix the minimum-energy configuration on a conical surface?1 questions

Domain of validity of the Lee–Levitov mechanical universality theorem for phyllotaxis: explicit characterization of the admissible potential family
Open for about 28 years

Do Fermi–Yang mesons exist?5 questions

The honeycomb-lattice Ising model1 questions

Exact solution and exact critical temperature of the spin-one Ising model on the honeycomb lattice
Open for about 53 years

The honeycomb-lattice Potts model1 questions

Disorder dependence of the phase-transition order in the two-dimensional q = 4 and q = 5 Potts models on the hexagonal lattice
Open for about 4 years

Honeycomb–triangular lattice duality1 questions

Full resummation of the direct triangular block condition for the symmetric-group permutation model
Open for less than 1 year

How do cofactors regulate protein structure and kinetic processes?8 questions

Ultrasound evaluation of early fatigue damage in composite materials9 questions

Multifrequency and frequency-tunable ultrasonic transducers3 questions

Closed-form scattering of an arbitrary number of bound states and quantum integrability of the O(2)L×O(2)RO(2)_L\times O(2)_RO(2)L​×O(2)R​ chiral Gross–Neveu (Zakharov–Mikhailov) model

The intertwiner property for non-diagonal factorizing S-matrices in the operator-algebraic inverse scattering construction

Physical realization of the extremal 2D S-matrix S=−SSGS=-S_{\mathrm{SG}}S=−SSG​ for a bound state with m1<2 mm_1<\sqrt{2}\,mm1​<2​m, and optimal coupling bounds away from integrable points

Completing the operator-algebraic renormalization construction of the critical two-dimensional Ising fixed point: reconciliation with the exact Ising QFT/CFT, sector structure, stability, and real-time dynamics

Completing the Painlevé VI characterization of the anisotropic Ising correlation C(M,N)C(M,N)C(M,N): boundary data, additive sigma decompositions, the M≥NM\geq NM≥N regime, and generic anisotropy

Critical behavior of the 2D Ising model with quasi-periodic coupling modulation beyond the weak-disorder regime: strong modulation, non-analytic modulations, and non-Diophantine frequencies

Critical frontier and disorder-strength dependence of the two-dimensional random-bond triangular Ising ferromagnet and the complementary random-bond three-state Potts case

Marginal quenched bond disorder in two-dimensional Ising systems: strong versus weak universality, crossover scales, and the universality of disorder-induced scaling

Existence of a nonlinear ordinary differential equation determining the row spin-spin correlation functions RnR_nRn​ of the two-dimensional Ising model

Painlevé VI equations for anisotropic Ising correlations: boundary-condition selection, the M≥NM\geq NM≥N regime at ν=−k\nu=-kν=−k, and generic anisotropy

Generalizing the boundary-limit transfer-matrix solution of the Brascamp-Kunz Ising model: fermion-parity sector projection and partition-function factorization on other lattices and boundary conditions

Disorder varieties of finite-support Ising-like models: characterizing restricted Perron eigenvectors of the transfer matrix and the exhaustiveness of the Khrapov parametrization

Quantitative microscopic account of the metal-insulator transition in the spinless two-valley two-dimensional electron system in ultraclean SiGe/Si/SiGe quantum wells

Microscopic foundation of the compressibility-driven scaling scenario for the two-dimensional metal-insulator transition: metallic-phase nature, stabilization against weak localization, and untested scaling predictions

Controlled incorporation of soft Wigner-crystal collective charge modes into the self-doping theory of the two-dimensional metal-insulator transition

Do true metals exist in two dimensions? Thermodynamic fate of the interaction-delocalized disordered two-dimensional electron gas

Universality of the two-parameter scaling description of the zero-field two-dimensional metal–insulator transition: critical exponents, critical resistivity, and the scaling function R(X,Y)

Why full spin polarization suppresses the resistivity-peak temperature Tmax⁡T_{\max}Tmax​ in the clean two-valley two-dimensional metal-insulator transition

Critical scaling of the insulating phase at the two-dimensional metal-insulator transition: which critical point governs Efros-Shklovskii hopping, and why is it unchanged by full spin polarization?

Fermi-surface reconstruction at the effective-mass-divergence density and the nature of the metallic state between ncn_cnc​ and nmn_mnm​ in ultra-clean SiGe/Si/SiGe two-dimensional electron systems

Quantitative separation of displacement and distribution-function mechanisms in microwave-induced resistance oscillations of realistic two-dimensional electron systems

Quantum-lifetime control of the microwave-induced zero-resistance state in unidirectional lateral superlattices

Current domains without external dc drive and their phonon-drag-voltage signatures in microwave-induced zero-resistance states of a two-dimensional electron gas

Microscopic theory of radiation-induced zero-conductance states in the nondegenerate two-dimensional electron system on liquid helium

Fluctuation effects, two-dimensional domain morphology, and global stability of the domain state in the voltage-biased zero-resistance state

Robustness and microscopic completion of the Franck–Condon-blockade mechanism for radiation-induced zero-resistance states in two-dimensional electron systems

Magnetotransport near the minimum-conductivity point of inhomogeneous graphene: the field-independent residual conductivity, the quantum-regime breakdown of effective-medium theory, and the puddle-versus-homogeneous origin of the ν=0\nu=0ν=0 Hall plateau

What sets the minimum conductivity of graphene at the charge-neutrality point: electron–hole hydrodynamic friction versus disorder-induced electron–hole puddles

The Dirac-point minimum conductivity of disordered graphene and its zero-temperature, thermodynamic-limit fate

Quantitative robustness of graphene's minimum-conductivity fan diagram: converged statistics, realistic disorder, and screening beyond the Gaussian-puddle model

Conductivity minimum of graphene with smooth particle-hole-asymmetric disorder in the intermediate-disorder regime

Exact thermodynamics of the two-dimensional square-lattice Ising model in a uniform external magnetic field

Rigorous analytic derivation of the electric critical exponents of the symmetric eight-vertex model (ηe=1−μ/π\eta_e = 1-\mu/\piηe​=1−μ/π, δe=(3π+μ)/(π−μ)\delta_e = (3\pi+\mu)/(\pi-\mu)δe​=(3π+μ)/(π−μ))

The true ground state and low-temperature phase diagram of PbZrO3: antiferroelectric or ferrielectric?

Defect- and Chemistry-Mediated Antiferroelectric-to-Ferroelectric Phase Conversion Under Electric-Field Cycling in HZO Thin Films: Coupling Explicit Defect Transport to Grain-Resolved Phase-Field Modeling

Completing the spectral theory of the degenerate chiral Potts models: eigenvectors and completeness, the k′=0k'=0k′=0 commuting Q-operator problem, and thermodynamics

Open issues in the Markov rate-equation description of filament-induced surface spiral turbulence in three-dimensional excitable media

Defect-mediated turbulence in the spatially extended Hastings–Powell period-doubling medium: pair-exchange mechanism, regimes beyond b1=3.5b_1=3.5b1​=3.5, three-dimensional states, and basin structure

Resonance-induced spiral-wave instability under weak localized periodic forcing: generality, mechanism, and predictive characterization

Nonlinear asymptotic stability of spiral waves in reaction–diffusion systems on the unbounded plane

Experimental verification that stretch-activated channels induce spiral-wave breakup in cardiac tissue at predicted mechano-electric thresholds

Anchoring-condition dependence of rotating spiral waves in driven curvature flow: frequency selection for non-orthogonal contact angles and bifurcations from dynamic anchoring

Validity limits and extensions of the virtual-filament effective dynamics of twisted and curved scroll waves in excitable media

Universality of spectral exponents and a Kolmogorov-like scaling theory for spiral- and scroll-wave turbulence in cardiac tissue

Non-equilibrium boundary-switching estimation of Ising interfacial tension: interface dynamics during switching, transverse boundary-condition finite-size effects, three-dimensional generalization, and efficiency versus interface cluster algorithms

Logarithmic finite-size effects on interfacial tension: the unresolved d=3d=3d=3 double-logarithmic correction, diffuse continuous-spin interfaces under antiperiodic boundaries, and the multiple-domain crossover

Continuity, random-current mixing, RSW crossing estimates, and the bulk Pfaffian structure for two-dimensional finite-range Ising models: the emergent-planarity open problems

The multirange Ising conjecture: does adding multiplicative interaction ranges on Zd\mathbb{Z}^dZd drive the critical coupling to that of a higher-dimensional Ising model?

Dimensional similarity of frustrated Ising magnetization: the untested simple-cubic prediction of Kassan-Ogly et al.

Completing the eigenvalue-amplitude theory of the Potts model on a torus: non-generic lattices, width-dependent level degeneracies, and the Beraha-number zero structure

Griffiths–Kelly–Sherman-type correlation inequalities for the eight-vertex model with non-uniform vertex weights

Exact finite-size correlation functions of the supersymmetric XYZ spin chain: Q-operator analyticity at the supersymmetric point, ground-state eigenvectors, further correlators, and the emergence of Painlevé VI

Checkerboard Z-invariant eight-vertex weights: completing the classification and going beyond the free-fermion manifold

Open directions for the R-matrix construction of non-invertible Kramers–Wannier symmetries: categorical precision, general-ppp fusion rules, and continuum limits of the induced critical lattice families

Extending the Kramers–Wannier duality to the series solutions and Painlevé VI equations of the two-dimensional Ising correlation functions

Kramers-Wannier critical-temperature equations beyond planarity: Tutte-polynomial duality for Ising and Potts models on non-planar lattices

Positivity, unimodality, real zeros, and the free-energy limit for the polynomials of the three-colour model with domain wall boundary conditions

Exact thermodynamic-limit value of proper xxx-colourings of the square lattice for x>3x>3x>3 (the square-lattice chromatic polynomial beyond q=3q=3q=3)

Analytic evaluation of the square-lattice k-coloring entropy W(k) beyond the exactly solved k=3 ice point: higher-cycle algebra, non-Eulerian subgraphs for k>3, and finite-width Toeplitz transfer-matrix recursions

Explicit closed-form evaluation of the partial partition functions of the three-coloring model with domain wall boundary conditions in the general elliptic case

Odd levels, the remaining non-reduced affine types, and the conceptual origin of the hidden SL2(Z)SL_2(\mathbb{Z})SL2​(Z)-symmetry in BCl(2)BC_l^{(2)}BCl(2)​ characters

Explicit fermionic-type character formulas for Feigin–Stoyanovsky type subspaces of standard sl(ℓ+1,C)∼\mathfrak{sl}(\ell+1,\mathbb{C})^{\sim}sl(ℓ+1,C)∼-modules in rank ℓ≥3\ell\geq 3ℓ≥3

Jacobian identities and polynomiality of invariant theta-function rings for the remaining affine Lie algebra types Dl(1)D_l^{(1)}Dl(1)​ and F4(1)F_4^{(1)}F4(1)​, E6(1)E_6^{(1)}E6(1)​, E6(2)E_6^{(2)}E6(2)​, E7(1)E_7^{(1)}E7(1)​, E8(1)E_8^{(1)}E8(1)​

Converses to modular invariance of characters: do modular-invariant characters force admissibility, rationality, and simplicity?

Exact solution theory of the non-diagonalisable spin chains from the non-difference-form regular 4×4 Yang–Baxter solutions

Non-perturbative construction of the generalized Chiral Potts model R-matrix from 4d Chern-Simons theory

Universal three-body spectrum of charged particles with resonant short-range interactions beyond the Born-Oppenheimer approximation: finite-mass-ratio corrections and the microscopic origin of the three-body parameter

Extending regularized Born-Oppenheimer molecular dynamics beyond the linear E⊗eE\otimes eE⊗e Jahn-Teller model: systematic Berry connections for polyatomic systems and quadratic vibronic coupling

Validity of the Born-Oppenheimer approximation for molecules in optical cavities when natural and light-induced conical intersections coexist

Separating adiabatic from nonadiabatic Born-Oppenheimer-breakdown corrections in alkali-metal dimers and reconciling ab initio mass shifts with near-threshold scattering

Nonadiabatic density-functional approximations and the time-dependent extension of exact molecular Kohn-Sham DFT beyond the Born-Oppenheimer approximation

Systematic nonadiabatic Kohn anomalies and phonon renormalization in three-dimensional heavily doped semiconductors and superconducting oxides, and their impact on electron-phonon coupling and superconducting TcT_cTc​ prediction

Modulated pairing states of mass-imbalanced Fermi superfluids: multi-wave-vector competition with the uniaxial Larkin-Ovchinnikov state and the full phase diagram

Stabilization, observability, and quantitative consequences of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in population-imbalanced Fermi superfluids

Power-law correlations in nonequilibrium steady states of gapped quantum spin chains: non-Toeplitz determinant asymptotics, robustness to interactions, and the unit-cell-doubling mechanism

Space-time duality approach to integrable quenches: exact characterisation of the fixed points of the space evolution and extension to equal-time two-point functions

Exact Euler-scale multi-point correlations in interacting integrable fluids out of equilibrium, and the singular regimes of the effective velocity

Rigorous foundation, multi-species generalization, multi-time extension, and convergence domain of the LeClair-Mussardo expansion for the Lieb-Liniger gas

Completing the exact solution of the eight-vertex model with quasi-periodic boundary conditions: odd-NNN completeness of the homogeneous TTT-QQQ ansatz, thermodynamic limit, and form factors

Scalar products of Bethe vectors in the 8-vertex model: undetermined normalization, imbalanced scalar products, and the form-factor program for the XYZ chain at rational anisotropy

Closed-form scattering of an arbitrary number of bound states and quantum integrability of the $O(2)_L\times O(2)_R$ chiral Gross–Neveu (Zakharov–Mikhailov) model

Physical realization of the extremal 2D S-matrix $S=-S_{\mathrm{SG}}$ for a bound state with $m_1<\sqrt{2}\,m$ , and optimal coupling bounds away from integrable points

Completing the Painlevé VI characterization of the anisotropic Ising correlation $C(M,N)$ : boundary data, additive sigma decompositions, the $M\geq N$ regime, and generic anisotropy

Existence of a nonlinear ordinary differential equation determining the row spin-spin correlation functions $R_n$ of the two-dimensional Ising model

Painlevé VI equations for anisotropic Ising correlations: boundary-condition selection, the $M\geq N$ regime at $\nu=-k$ , and generic anisotropy

Why full spin polarization suppresses the resistivity-peak temperature $T_{\max}$ in the clean two-valley two-dimensional metal-insulator transition

Fermi-surface reconstruction at the effective-mass-divergence density and the nature of the metallic state between $n_c$ and $n_m$ in ultra-clean SiGe/Si/SiGe two-dimensional electron systems

Magnetotransport near the minimum-conductivity point of inhomogeneous graphene: the field-independent residual conductivity, the quantum-regime breakdown of effective-medium theory, and the puddle-versus-homogeneous origin of the $\nu=0$ Hall plateau

Rigorous analytic derivation of the electric critical exponents of the symmetric eight-vertex model ( $\eta_e = 1-\mu/\pi$ , $\delta_e = (3\pi+\mu)/(\pi-\mu)$ )

Completing the spectral theory of the degenerate chiral Potts models: eigenvectors and completeness, the $k'=0$ commuting Q-operator problem, and thermodynamics

Defect-mediated turbulence in the spatially extended Hastings–Powell period-doubling medium: pair-exchange mechanism, regimes beyond $b_1=3.5$ , three-dimensional states, and basin structure

Logarithmic finite-size effects on interfacial tension: the unresolved $d=3$ double-logarithmic correction, diffuse continuous-spin interfaces under antiperiodic boundaries, and the multiple-domain crossover

The multirange Ising conjecture: does adding multiplicative interaction ranges on $\mathbb{Z}^d$ drive the critical coupling to that of a higher-dimensional Ising model?

Open directions for the R-matrix construction of non-invertible Kramers–Wannier symmetries: categorical precision, general- $p$ fusion rules, and continuum limits of the induced critical lattice families

Exact thermodynamic-limit value of proper $x$ -colourings of the square lattice for $x>3$ (the square-lattice chromatic polynomial beyond $q=3$ )

Odd levels, the remaining non-reduced affine types, and the conceptual origin of the hidden $SL_2(\mathbb{Z})$ -symmetry in $BC_l^{(2)}$ characters

Explicit fermionic-type character formulas for Feigin–Stoyanovsky type subspaces of standard $\mathfrak{sl}(\ell+1,\mathbb{C})^{\sim}$ -modules in rank $\ell\geq 3$

Jacobian identities and polynomiality of invariant theta-function rings for the remaining affine Lie algebra types $D_l^{(1)}$ and $F_4^{(1)}$ , $E_6^{(1)}$ , $E_6^{(2)}$ , $E_7^{(1)}$ , $E_8^{(1)}$

Extending regularized Born-Oppenheimer molecular dynamics beyond the linear $E\otimes e$ Jahn-Teller model: systematic Berry connections for polyatomic systems and quadratic vibronic coupling

Systematic nonadiabatic Kohn anomalies and phonon renormalization in three-dimensional heavily doped semiconductors and superconducting oxides, and their impact on electron-phonon coupling and superconducting $T_c$ prediction

Completing the exact solution of the eight-vertex model with quasi-periodic boundary conditions: odd- $N$ completeness of the homogeneous $T$ - $Q$ ansatz, thermodynamic limit, and form factors

Constraining the annihilation optical potential and pole content of quark-model coupled-channel $p\bar p$ scattering: do the predicted near-threshold poles correspond to the observed $X(1835)$ -family states?

The baryonium interpretation of the X(1835): establishing a near-threshold nucleon-antinucleon ${}^{11}S_0$ bound state and its decay pattern