物理学｜格物 GEWU

二体

S

矩阵3 个问题

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

二维 Ising 的 Toeplitz/Pfaffian 关联函数结构2 个问题

二维 Ising 临界指数3 个问题

二维 Ising 与 Painlevé 方程2 个问题

二维 Ising 转移矩阵谱2 个问题

二维电子系统在零磁场下的金属-绝缘体转变问题8 个问题

二维电子系统在微波辐照下的零电阻现象6 个问题

二维石墨中的电导率极小问题5 个问题

二维一般非零均匀磁场 Ising 未解问题1 个问题

Exact thermodynamics of the two-dimensional square-lattice Ising model in a uniform external magnetic field
未解决约 82 年

二自旋和四自旋 Ising 表示1 个问题

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

反铁电相（antiferroelectric phase）2 个问题

反演关系（inversion relations）1 个问题

Completing the spectral theory of the degenerate chiral Potts models: eigenvectors and completeness, the $k'=0$ commuting Q-operator problem, and thermodynamics
未解决约 18 年

反应扩散系统中螺旋波的失稳机制8 个问题

反周期边界与界面张力2 个问题

方格 Ising 模型3 个问题

方格 Potts 模型1 个问题

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
未解决约 20 年

方格八顶点模型（eight-vertex model）3 个问题

方格高低温对偶3 个问题

方格三着色问题4 个问题

仿射 Lie 代数字符4 个问题

非 difference-property 模型2 个问题

非玻恩-奥本海默近似问题6 个问题

非均匀费米超流体的FFLO态2 个问题

非平衡关联函数4 个问题

非齐次八顶点模型4 个问题

非线性波传播的界面效应8 个问题

非线性积分方程3 个问题

非线性驻波声场的数学模型和理论6 个问题

菲波纳契双螺旋是锥面上的最小能量构型吗？1 个问题

Domain of validity of the Lee–Levitov mechanical universality theorem for phyllotaxis: explicit characterization of the admissible potential family
未解决约 28 年

费米-杨介子存在吗？5 个问题

蜂窝格 Ising 模型1 个问题

Exact solution and exact critical temperature of the spin-one Ising model on the honeycomb lattice
未解决约 53 年

蜂窝格 Potts 模型1 个问题

Disorder dependence of the phase-transition order in the two-dimensional q = 4 and q = 5 Potts models on the hexagonal lattice
未解决约 4 年

蜂窝格—三角格对偶1 个问题

Full resummation of the direct triangular block condition for the symmetric-group permutation model
未解决不足 1 年

辅助因子如何调控的蛋白质结构与动力学过程？8 个问题

复合材料早期疲劳损伤的超声评价9 个问题

复频及频率可调超声换能器3 个问题

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