GEWU Magazine

generalized Gibbs ensemble3 questions

Deep thermalization in interacting integrable quantum systems: constructing the analogue of the deep generalized Gibbs ensemble beyond free fermions
Extending the nonlinear integral equation formulation of the sine-Gordon generalized Gibbs ensemble beyond the individual-boundedness restriction
Determining the number of Lagrange multipliers needed for generalized Gibbs ensemble descriptions of realistic integrable quantum systems

generalized hydrodynamics（GHD）2 questions

Hall–Littlewood and

q

-Whittaker process2 questions

Hard Hexagon and Related Models7 questions

Hard-hexagon critical activity3 questions

Hard-hexagon critical exponent3 questions

Hard-hexagon model3 questions

Hard-hexagon order parameter2 questions

Hard-square model4 questions

Hecke algebra1 questions

Polynomial integrability of the Temperley-Lieb loop model: non-degenerate principal-Hamiltonian spectra and the transfer-operator-to-Hamiltonian decomposition for all system sizes
Open for about 4 years

height function3 questions

higher-order TRG3 questions

Ice-Type Models4 questions

impurity models1 questions

Ferromagnetic-impurity and gapless-bulk regimes of the exactly solved Kondo impurity at the edge of a superconducting wire

infinite PEPS3 questions

interacting particle systems1 questions

Open problems for the boundary-driven zero-range process with long jumps: hydrodynamic limits and dynamical large deviations, boundary asymptotics of the hydrostatic profile, and the critical and condensation regimes

intertwiner3 questions

IRF/face model2 questions

Ising Model on the Bethe Lattice5 questions

Ising–dimer mapping3 questions

Ising/free-fermion special case1 questions

Free-fermion diagonalisation of the 8-vertex class-B chain at arbitrary length N, and the generality of the free-fermion condition for integrable R-matrices
Open for about 5 years

Izergin–Korepin determinant4 questions

Jacobi elliptic functions1 questions

Elementary magnitude bounds for Jacobian elliptic functions with complex modulus beyond the regime $|m|\le1$ , $|z|<\pi/2$

Kagomé eight-vertex model1 questions

Adjudicating conflicting exact spontaneous-magnetization formulae for the isotropic kagomé Ising lattice and deriving the closed-form anisotropic magnetization

Kagomé lattice Ising-type model2 questions

Kagomé Lattice Eight-Vertex Model2 questions

Kagomé–square lattice model transformation3 questions

Kasteleyn orientation2 questions

KPZ universality class3 questions

Kramers–Wannier duality4 questions

Landen transformation3 questions

Lee–Yang model2 questions

limit shape3 questions

Loop model and conformal field theory1 questions

Rigorous proof of the closed-form three-point structure constants of critical loop models for all allowed Kac labels

Has Lorentz symmetry been broken?5 questions

Macdonald processes3 questions

Deep thermalization in interacting integrable quantum systems: constructing the analogue of the deep generalized Gibbs ensemble beyond free fermions

Extending the nonlinear integral equation formulation of the sine-Gordon generalized Gibbs ensemble beyond the individual-boundedness restriction

Determining the number of Lagrange multipliers needed for generalized Gibbs ensemble descriptions of realistic integrable quantum systems

Quantum Generalized Hydrodynamics beyond the quadratic, zero-entropy, Euler-scale regime

Rigorous emergence of generalised hydrodynamics in generalised TTˉT\bar{T}TTˉ-deformed classical free-particle systems with arbitrary two-body scattering shifts

Bulk Gaussian (Edwards–Wilkinson) scaling limits of the (2+1)(2+1)(2+1)-dimensional qqq-Whittaker growth model at fixed q∈(0,1)q\in(0,1)q∈(0,1)

Bijective proofs, algebraic structure, ubiquity, and quasi-open six-vertex asymptotics for the free-boundary q-Whittaker and Hall-Littlewood symmetry identities

Algorithmic Pirogov–Sinai theory at the phase boundary: efficient counting and sampling in the phase-coexistence regime for lattice models

Phase diagram of the loop O(n)O(n)O(n) model with large nnn and its hard-hexagon limit

Global analytic structure of the hard-hexagon partition function per site in the complex fugacity plane: dominant eigenvalue branches beyond Baxter's solution

Exact evaluation of the entropy W(k)W(k)W(k) of kkk-colorings of the square lattice (kkk-species close-packed hard-square lattice gas): vertex-model, transfer-matrix, and graph-expansion routes

Controlled determination of the critical parameters of the disordered-columnar transition in the 2x2 hard-square (2-NN exclusion) lattice gas

Higher-order terms, convergence, and quantitative validity of the high-activity z−1/2z^{-1/2}z−1/2 expansion for the hard square lattice gas with nearest- and next-nearest-neighbor exclusion

Common crossing of finite-width density curves at the critical point of the hard-square lattice gas

Localized-magnon saturation physics of frustrated antiferromagnets beyond the smallest-area hard-core description: extra ground states, residual entropy, hard-square thermodynamics, and microscopic U and V parameters

Nonunitary string-net PEPS: tube-algebra central idempotents without C*-structure, gapped non-Hermitian parent Hamiltonians, convergent fixed-point algorithms, and extensions to logarithmic CFTs

Limits of the R-matrix analysis of Mayer cluster coefficients: the spectrum-shift regime, reality of the matrix elements, and error-controlled critical activities

Thermodynamic-limit analytic structure of the non-integrable hard-square lattice gas: zero locus, equimodular gaps, the z=−1z=-1z=−1 conjectures, and a discriminant criterion for integrability

Critical exponents from Mayer cluster coefficients: completing the R-matrix asymptotic theory beyond its validated range

Analytic structure of the hard-hexagon partition function per site in the complex fugacity plane: dominant transfer-matrix eigenvalue branches, the necklace region and its zeros, and the algebraic origin of the extra eigenvalues

Conjectural foundations of the inversion-relation solution for solvable IRF lattice models: thermalization, analyticity of the free energy, and the unidentified coset CFT G\mathcal{G}G

Thermodynamic-limit analytic structure of the hard-hexagon partition function at complex fugacity: the necklace of zeros and the transfer-matrix eigenvalue branches beyond Baxter's solution

Exact entanglement characterization of the Rokhsar-Kivelson quantum hard-square lattice gas: Rényi entropies, integrable entanglement spectra, and the extension beyond two-leg ladders

Fine structure of the available-site fraction in the exactly solved hard-hexagon model near the phase transition

Hard-hexagon partition function for complex fugacity: thermodynamic-limit persistence of the zero necklace and transfer-matrix eigenvalue branches beyond Baxter's solution

Melting scenario of the period-3 phase of the hard-square model with diagonal interactions: Lifshitz point location, anisotropic critical exponents, and floating-phase boundaries

Exact values of the hard-square entropy constant and the bipartite hard-square constant for grid-graph independent-set enumeration

Existence, sharpness, and location of the uniqueness threshold of the hard-core lattice gas on the square lattice Z2\mathbb{Z}^2Z2 (conjectured λc(Z2)≈3.796\lambda_c(\mathbb{Z}^2)\approx 3.796λc​(Z2)≈3.796)

Unresolved phase diagram, Gibbs-measure classification, and sharp correlation decay for the 2×22\times22×2 hard-square lattice gas

Polynomial integrability of the Temperley-Lieb loop model: non-degenerate principal-Hamiltonian spectra and the transfer-operator-to-Hamiltonian decomposition for all system sizes

Asymptotic variance constant and Gaussian scaling limits for the square-ice height function and generalized solid-on-solid models

Disorder-induced regions and the height-function scaling limit in the square-lattice dimer model with layered quenched disorder

Uniqueness of limit shapes for the six-vertex model with rare corners and restricted Mallows permutations at general bias

Systematically improvable three-dimensional tensor-network renormalization group: controlled entanglement filtering of the area-law obstruction and extraction of universal data in 3D lattice models

Grassmann tensor-network coarse-graining for four-dimensional lattice QCD: full gauge-fermion treatment with controlled truncation accuracy

Provable error bounds for randomized higher-order tensor renormalization group methods (R-HOTRG, MDTRG, Triad-MDTRG)

Residual entropy of ordinary ice: the exact ice-rule configuration count and a precision experimental test of Pauling's estimate

Continuum limit of the Feynman checkerboard model as a complex-weight six-vertex model in an absorbing strip

Approximation complexity of the six-vertex model in the white region and on planar graphs

Exact growth constant for colourings of the square lattice with more than three colours

Ferromagnetic-impurity and gapless-bulk regimes of the exactly solved Kondo impurity at the edge of a superconducting wire

Parent Hamiltonian and Gossamer-Tail Control for Chiral Projected Entangled-Pair States: Bulk Gaps of the Z3 Kitaev Chiral Spin Liquid

Certified extraction of anyon sectors and modular data from infinite PEPS: completeness of transfer-matrix fixed points and correlation-length scaling

Decidability of normalizability, symmetry classification, canonical forms, and the parent-Hamiltonian spectral gap within physically relevant subclasses of projected entangled pair states

Open problems for the boundary-driven zero-range process with long jumps: hydrodynamic limits and dynamical large deviations, boundary asymptotics of the hydrostatic profile, and the critical and condensation regimes

The periodic-diffeomorphism case of the intertwiner volume conjecture for the Kauffman bracket skein algebra

Completing the theory of vertical (particle-number-changing) intertwiners in the rational Calogero model

Completing the permutation-coefficient theory of gl(n) Yangian intertwiners: general parameter permutations, general rank and evaluation order, contour dependence, and factorization equivalence

Constructing quantum R-matrix blocks in tensor-product multiplicity sectors and rederiving them from rational CFT data

Factorization of reduced density matrices and closed representations of the nearest-neighbour two-point function in integrable face models

Extremality of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree

Analytic classification of the invariant sets, positive fixed points, and higher-period orbits of the recursion operator for the Ising model with competing binary and ternary interactions on a third-order Cayley tree

Exactness of closed-form self-consistent equations for the bond-diluted Ising model on the Bethe lattice

Exact solution of the quenched bond-diluted Ising model on the Bethe lattice at finite coupling (p<1p<1p<1, q>2q>2q>2)

Validity and explanatory power of the finite-variable reduced dynamics for Glauber dynamics of the bond-diluted Ising model on a Bethe lattice

Explicit identification of the local and Fourier inverse Kasteleyn matrices for the critical Z-invariant Ising model on periodic isoradial graphs

Completing exact bosonization of the critical Ising model in bounded domains: flat-boundary dimer observables, the half-integer electric endpoint, and lattice-to-continuum constants

A general structural theory for dimer models on non-bipartite periodic graphs: weak limits of Boltzmann measures and spectral curves

Free-fermion diagonalisation of the 8-vertex class-B chain at arbitrary length N, and the generality of the free-fermion condition for integrable R-matrices

Basis-parametrized determinant representations for the six-vertex model with partial domain wall boundary conditions

Extending the modified-operator linear-system method for six-vertex partition functions to reflecting boundaries, the trigonometric antiperiodic case, and higher rank

The Izergin–Korepin nineteen-vertex domain wall partition function beyond the root of unity: closed forms, reflection boundaries, eigenvector components, and structural characterization

Six-vertex domain-wall partition function at roots of unity beyond the third: functional-equation evaluation

Elementary magnitude bounds for Jacobian elliptic functions with complex modulus beyond the regime ∣m∣≤1|m|\le1∣m∣≤1, ∣z∣<π/2|z|<\pi/2∣z∣<π/2

Adjudicating conflicting exact spontaneous-magnetization formulae for the isotropic kagomé Ising lattice and deriving the closed-form anisotropic magnetization

Microscopic origin of the anomalous critical scattering at the kagome-ice plateau termination in Ho2Ti2O7 under a tilted [111] field

Exact finite-temperature characterization of the disordered regions of the generalized kagomé-lattice Ising model with pair and triplet interactions

Open problems for the free-fermion eight-vertex models on the square lattice: singularities of staggered free-fermion models, invariant variables, and the general even–odd finite-torus mapping

Universality classes of the non-Ising transitions in the six-vertex model on the kagome lattice

Exact or provably controlled quantum decoration transformations for non-commuting quantum spin lattice models

Explicit Kagome-type decorated-lattice construction from the gauge/YBE decoration transformation and its place in the integrability web

Yang-Baxter integrability of the 3D quantum crystal melting Hamiltonian: Kagome-lattice Boltzmann weights, a commuting transfer matrix, and the mass-gap conjecture

The Pfaffian recognition problem beyond planar, bipartite, and near-bipartite graphs (Problem 42 of Kothari–de Carvalho–Lucchesi–Little)

Extending the Pfaffian Sign Theorem for the dimer model to other lattices on the torus and to higher-genus and non-orientable surfaces

Boundaries of Kardar-Parisi-Zhang universality for the chronon in time-crystalline matter

Simultaneous Hausdorff dimension of the geodesic splitting sets in the directed landscape across all time levels

Exact solvability, stationary structure, and KPZ universality of the quantum ASEP and its quantum Kardar-Parisi-Zhang dynamics

Sector dependence of the exact Kramers–Wannier duality in exactly solvable SO(nnn) spin chains: the Ramond sector and its Spin(nnn)1_11​ duality-defect interpretation

Generalizing non-invertible Kramers-Wannier and Kennedy-Tasaki transformations beyond one dimension: higher-form gauging, SSPT classification beyond two dimensions, the fermionic exchange origin, and non-invertible Lieb-Schultz-Mattis constraints

Self-dual Kramers-Wannier points as non-invertible symmetries: phase transitions and criticality of LDPC codes in non-Euclidean geometries

Rigorous emergence of generalised hydrodynamics in generalised $T\bar{T}$ -deformed classical free-particle systems with arbitrary two-body scattering shifts

Bulk Gaussian (Edwards–Wilkinson) scaling limits of the $(2+1)$ -dimensional $q$ -Whittaker growth model at fixed $q\in(0,1)$

Phase diagram of the loop $O(n)$ model with large $n$ and its hard-hexagon limit

Exact evaluation of the entropy $W(k)$ of $k$ -colorings of the square lattice ( $k$ -species close-packed hard-square lattice gas): vertex-model, transfer-matrix, and graph-expansion routes

Higher-order terms, convergence, and quantitative validity of the high-activity $z^{-1/2}$ expansion for the hard square lattice gas with nearest- and next-nearest-neighbor exclusion

Thermodynamic-limit analytic structure of the non-integrable hard-square lattice gas: zero locus, equimodular gaps, the $z=-1$ conjectures, and a discriminant criterion for integrability

Conjectural foundations of the inversion-relation solution for solvable IRF lattice models: thermalization, analyticity of the free energy, and the unidentified coset CFT $\mathcal{G}$

Existence, sharpness, and location of the uniqueness threshold of the hard-core lattice gas on the square lattice $\mathbb{Z}^2$ (conjectured $\lambda_c(\mathbb{Z}^2)\approx 3.796$ )

Unresolved phase diagram, Gibbs-measure classification, and sharp correlation decay for the $2\times2$ hard-square lattice gas

Exact solution of the quenched bond-diluted Ising model on the Bethe lattice at finite coupling ( $p<1$ , $q>2$ )

Elementary magnitude bounds for Jacobian elliptic functions with complex modulus beyond the regime $|m|\le1$ , $|z|<\pi/2$

Sector dependence of the exact Kramers–Wannier duality in exactly solvable SO( $n$ ) spin chains: the Ramond sector and its Spin( $n$ ) $_1$ duality-defect interpretation

Smoothness of multinomial dimer limit shapes in dimensions $d>2$ (Kenyon-Wolfram, Question 10.2)

Fredholm determinantal representations and asymptotics of periodic Macdonald processes at positive charge $u>0$