Scientists / Open questions

Giorgio Parisi

Statistical physics; disordered and complex systems

2021 Nobel Prize in Physics

166 questions

Growth law, temperature dependence, and geometry of the dynamical correlation length in aging structural glasses
The fate of the Gardner transition in finite-dimensional structural glasses: existence, finite-size extrapolation, and experimental detection beyond the mean-field Mari-Kurchan model
Hessian spectrum and low-energy mode localization in the replica-symmetry-broken phase of the fully-connected vector spin glass in a random field
The upper critical dimension of the Kardar-Parisi-Zhang universality class
Causal mechanisms and directed influence structure underlying the cross-correlations of American baby names
Mathematical foundations and validity boundary of the complex Langevin method for complex-valued path-integral weights
Statistical-mechanical open problems for the most compact regular lattices in large dimensions: the asymptotics of the maximal reduced packing radius $r_M$ and the lattice-versus-amorphous question (Parisi, 2008)
Open analytic problems for the instantaneous normal mode spectrum of low-density liquids: closed-form tail coefficient, extension to $d>1$ , and localization edges
Two-loop instanton correction to the large-order behavior of the 2M-point Green functions of φ⁴ theory in d = 2 and 3, and its use in Borel–conformal resummation of critical exponents
Validity of the single-point quenched reduction of large- $N$ lattice gauge theory: equivalence with the infinite-volume Wilson theory at intermediate couplings and in the approach to the continuum limit, and exact solution of the reduced few-matrix models
Domain of validity of threshold-resummed leading-twist QCD at large x: the crossover to higher-twist dominance in deep-inelastic scattering and Drell-Yan
Finite-size ( $1/N$ ) corrections to the number of TAP solutions in the Sherrington–Kirkpatrick spin glass: the vanishing-prefactor problem of the Bray–Moore complexity
Fate of the Parisi-Slanina hard-sphere toy model above the critical density $\rho_{1c}=1-\ln 2$ in the infinite-dimensional limit
Systematic control of the $1/M$ loop expansion around the Bethe approximation: subleading corrections, degenerate critical spectra, and finite- $M$ spurious disorder in the M-layer construction
Replica-symmetry breaking, coefficients, and detectability in Parisi's analysis of microscopic random energy-momentum non-conservation
Activated processes and the four-point dynamical susceptibility of supercooled liquids: rounding the mean-field divergence of $\chi_4$ and its correlation length at the mode-coupling transition
Finite-dimensional fate of the Franz-Parisi coupled-replica phase diagram of glass formers: coexistence line, critical endpoint, and the connection to a thermodynamic glass transition at zero coupling
Freezing (Kauzmann) transition and low-temperature phase of the hierarchical random energy model and its p-spin generalization
Dimension dependence of the constrained overlap correlation function in the Ising spin glass: reconciling the Franz-Parisi-Virasoro interface theory with the high-dimensional mean-field expansion
Existence and nature of the de Almeida–Thouless transition in the three-dimensional Edwards–Anderson spin glass in a magnetic field
Completing the first-principles replica theory of structural glasses: activated processes, dynamics, and quantitative liquid-state input
Existence, nature, and universality class of the random-pinning glass transition in a three-dimensional Lennard-Jones glass former
Rigorous correspondence between classical saddles and Borel-plane singularities in renormalized interacting quantum field theories (the surviving core of the Parisi-Lipatov large-order program)
Finite-dimensional realization of overlap-phase coexistence, the Maxwell construction, and metastable-decay dynamics in the Franz-Parisi effective potential of glassy systems

Back to open problems

Growth law, temperature dependence, and geometry of the dynamical correlation length in aging structural glasses

The fate of the Gardner transition in finite-dimensional structural glasses: existence, finite-size extrapolation, and experimental detection beyond the mean-field Mari-Kurchan model

Hessian spectrum and low-energy mode localization in the replica-symmetry-broken phase of the fully-connected vector spin glass in a random field

The upper critical dimension of the Kardar-Parisi-Zhang universality class

Causal mechanisms and directed influence structure underlying the cross-correlations of American baby names

Mathematical foundations and validity boundary of the complex Langevin method for complex-valued path-integral weights

Statistical-mechanical open problems for the most compact regular lattices in large dimensions: the asymptotics of the maximal reduced packing radius rMr_MrM​ and the lattice-versus-amorphous question (Parisi, 2008)

Open analytic problems for the instantaneous normal mode spectrum of low-density liquids: closed-form tail coefficient, extension to d>1d>1d>1, and localization edges

Two-loop instanton correction to the large-order behavior of the 2M-point Green functions of φ⁴ theory in d = 2 and 3, and its use in Borel–conformal resummation of critical exponents

Validity of the single-point quenched reduction of large-NNN lattice gauge theory: equivalence with the infinite-volume Wilson theory at intermediate couplings and in the approach to the continuum limit, and exact solution of the reduced few-matrix models

Domain of validity of threshold-resummed leading-twist QCD at large x: the crossover to higher-twist dominance in deep-inelastic scattering and Drell-Yan

Finite-size (1/N1/N1/N) corrections to the number of TAP solutions in the Sherrington–Kirkpatrick spin glass: the vanishing-prefactor problem of the Bray–Moore complexity

Fate of the Parisi-Slanina hard-sphere toy model above the critical density ρ1c=1−ln⁡2\rho_{1c}=1-\ln 2ρ1c​=1−ln2 in the infinite-dimensional limit

Systematic control of the 1/M1/M1/M loop expansion around the Bethe approximation: subleading corrections, degenerate critical spectra, and finite-MMM spurious disorder in the M-layer construction

Replica-symmetry breaking, coefficients, and detectability in Parisi's analysis of microscopic random energy-momentum non-conservation

Activated processes and the four-point dynamical susceptibility of supercooled liquids: rounding the mean-field divergence of χ4\chi_4χ4​ and its correlation length at the mode-coupling transition

Finite-dimensional fate of the Franz-Parisi coupled-replica phase diagram of glass formers: coexistence line, critical endpoint, and the connection to a thermodynamic glass transition at zero coupling

Freezing (Kauzmann) transition and low-temperature phase of the hierarchical random energy model and its p-spin generalization

Dimension dependence of the constrained overlap correlation function in the Ising spin glass: reconciling the Franz-Parisi-Virasoro interface theory with the high-dimensional mean-field expansion

Existence and nature of the de Almeida–Thouless transition in the three-dimensional Edwards–Anderson spin glass in a magnetic field

Completing the first-principles replica theory of structural glasses: activated processes, dynamics, and quantitative liquid-state input

Existence, nature, and universality class of the random-pinning glass transition in a three-dimensional Lennard-Jones glass former

Rigorous correspondence between classical saddles and Borel-plane singularities in renormalized interacting quantum field theories (the surviving core of the Parisi-Lipatov large-order program)

Finite-dimensional realization of overlap-phase coexistence, the Maxwell construction, and metastable-decay dynamics in the Franz-Parisi effective potential of glassy systems

Statistical-mechanical open problems for the most compact regular lattices in large dimensions: the asymptotics of the maximal reduced packing radius $r_M$ and the lattice-versus-amorphous question (Parisi, 2008)

Open analytic problems for the instantaneous normal mode spectrum of low-density liquids: closed-form tail coefficient, extension to $d>1$ , and localization edges

Validity of the single-point quenched reduction of large- $N$ lattice gauge theory: equivalence with the infinite-volume Wilson theory at intermediate couplings and in the approach to the continuum limit, and exact solution of the reduced few-matrix models

Finite-size ( $1/N$ ) corrections to the number of TAP solutions in the Sherrington–Kirkpatrick spin glass: the vanishing-prefactor problem of the Bray–Moore complexity

Fate of the Parisi-Slanina hard-sphere toy model above the critical density $\rho_{1c}=1-\ln 2$ in the infinite-dimensional limit

Systematic control of the $1/M$ loop expansion around the Bethe approximation: subleading corrections, degenerate critical spectra, and finite- $M$ spurious disorder in the M-layer construction

Activated processes and the four-point dynamical susceptibility of supercooled liquids: rounding the mean-field divergence of $\chi_4$ and its correlation length at the mode-coupling transition