Michael Aizenman | Academic Influence

Michael Aizenman's AcademicInfluence.com Rankings

Michael Aizenman

Mathematics

#627

World Rank

#1167

Historical Rank

#275

USA Rank

Measure Theory

#1031

World Rank

#1328

Historical Rank

#380

USA Rank

mathematics Degrees

Michael Aizenman

Physics

#1175

World Rank

#1849

Historical Rank

#518

USA Rank

physics Degrees

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Mathematics
Physics

Michael Aizenman's Degrees

PhD Physics Princeton University
Bachelors Physics Tel Aviv University

Why Is Michael Aizenman Influential?

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According to Wikipedia, Michael Aizenman is an American-Israeli mathematician and a physicist at Princeton University, working in the fields of mathematical physics, statistical mechanics, functional analysis and probability theory.

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Michael Aizenman's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Fractals: Form, Chance and Dimension (1978) (3000)
Localization at large disorder and at extreme energies: An elementary derivations (1993) (611)
Sharpness of the phase transition in percolation models (1987) (392)
Brownian motion and harnack inequality for Schrödinger operators (1982) (388)
Rounding of first-order phase transitions in systems with quenched disorder. (1989) (353)
Geometric analysis of φ4 fields and Ising models. Parts I and II (1982) (341)
Discontinuity of the magnetization in one-dimensional 1/¦x−y¦2 Ising and Potts models (1988) (329)
LOCALIZATION AT WEAK DISORDER: SOME ELEMENTARY BOUNDS (1994) (286)
Proof of the Triviality of ϕ d 4 Field Theory and Some Mean-Field Features of Ising Models for d > 4 (1981) (285)
Tree graph inequalities and critical behavior in percolation models (1984) (262)
Rounding effects of quenched randomness on first-order phase transitions (1990) (235)
Geometric analysis of ϕ 4 fields and Ising models (1982) (218)
Finite-Volume Fractional-Moment Criteria¶for Anderson Localization (1999) (204)
Localization bounds for an electron gas (1996) (203)
Holder Regularity and Dimension Bounds for Random Curves (1998) (190)
Some rigorous results on the Sherrington-Kirkpatrick spin glass model (1987) (177)
Moment analysis for localization in random Schrödinger operators (2003) (176)
On the Stability of the Quenched State in Mean-Field Spin-Glass Models (1997) (172)
Extended variational principle for the Sherrington-Kirkpatrick spin-glass model (2003) (166)
Discontinuity of the percolation density in one dimensional 1/|x−y|2 percolation models (1986) (163)
Translation invariance and instability of phase coexistence in the two dimensional Ising system (1980) (161)
Convergence to equilibrium in a system of reacting polymers (1979) (159)
Metastability effects in bootstrap percolation (1988) (155)
Geometric aspects of quantum spin states (1993) (147)
Strict monotonicity for critical points in percolation and ferromagnetic models (1991) (143)
Random Operators: Disorder Effects on Quantum Spectra and Dynamics (2015) (141)
On the critical behavior of the magnetization in high-dimensional Ising models (1986) (134)
On semi-classical bounds for eigenvalues of Schrödinger operators (1978) (133)
On the Number of Incipient Spanning Clusters (1996) (132)
Percolation Critical Exponents Under the Triangle Condition (1991) (123)
Stability of the Absolutely Continuous Spectrum of Random Schrödinger Operators on Tree Graphs (2005) (113)
Localization Bounds for Multiparticle Systems (2008) (110)
Random Currents and Continuity of Ising Model’s Spontaneous Magnetization (2013) (109)
The phase boundary in dilute and random Ising and Potts ferromagnets (1987) (107)
Resonant delocalization for random Schr\"odinger operators on tree graphs (2011) (97)
On the structure of quasi-stationary competing particle systems (2007) (95)
Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder (2005) (92)
Path Crossing Exponents and the External Perimeter in 2D Percolation (1999) (90)
An Extended Variational Principle for the SK Spin-Glass Model (2003) (85)
Characterization of invariant measures at the leading edge for competing particle systems (2004) (84)
On the renormalized coupling constant and the susceptibility in φ44 field theory and the Ising model in four dimensions (1983) (80)
Rapid Convergence to Equilibrium of Stochastic Ising Models in the Dobrushin Shlosman Regime (1987) (78)
Scaling limits for minimal and random spanning trees in two dimensions (1998) (78)
Bose-Einstein quantum phase transition in an optical lattice model (2004) (77)
The Canopy Graph and Level Statistics for Random Operators on Trees (2006) (75)
Fluctuations of extensive functions of quenched random couplings (1990) (75)
Structure of gibbs states of one dimensional Coulomb systems (1980) (73)
Marginal triviality of the scaling limits of critical 4D Ising and 𝜑44 models (2019) (59)
The Creation of Spectral Gaps by Graph Decoration (2000) (58)
The intersection of Brownian paths as a case study of a renormalization group method for quantum field theory (1985) (58)
Some rigorous results on the Sherrington-Kirkpatrick spin glass model (1987) (58)
The third law of thermodynamics and the degeneracy of the ground state for lattice systems (1981) (56)
MEAN-FIELD SPIN GLASS MODELS FROM THE CAVITY-ROST PERSPECTIVE (2006) (55)
On vector fields as generators of flows: A counterexample to Nelson's conjecture (1978) (54)
Scaling Limit for the Incipient Spanning Clusters (1996) (51)
Percolation methods for disordered quantum Ising models (1993) (49)
On Bernoulli decompositions for random variables, concentration bounds, and spectral localization (2007) (48)
Lower bounds on the cluster size distribution (1980) (43)
Stability and equilibrium states of infinite classical systems (1976) (41)
Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs (2012) (38)
Ergodic properties of an infinite one dimensional hard rod system (1975) (38)
Magnetic properties of some itinerant-electron systems at T>0. (1990) (36)
Extended states in a Lifshitz tail regime for random Schrödinger operators on trees. (2010) (36)
Ergodic Theory in Statistical Mechanics. (1975) (35)
Conditional equilibrium and the equivalence of microcanonical and grandcanonical ensembles in the thermodynamic limit (1978) (35)
On the slow decay ofO(2) correlations in the absence of topological excitations: Remark on the Patrascioiu-Seiler model (1994) (34)
Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder (2011) (33)
Local Ward identities and the decay of correlations in ferromagnets (1980) (32)
Critical exponents for long-range interactions (1988) (31)
Rounding of first order transitions in low-dimensional quantum systems with quenched disorder. (2009) (31)
Percolation of the minority spins in high-dimensional Ising models (1987) (30)
Complete Dynamical Localization in Disordered Quantum Multi-Particle Systems (2009) (28)
From Finite-System Entropy to Entropy Rate for a Hidden Markov Process (2005) (26)
Erratum: Rounding of first-order phase transitions in systems with quenched disorder [Phys. Rev. Lett. 62, 2503 (1989)] (1990) (25)
Ergodic properties of infinite systems (1975) (25)
Emergent planarity in two-dimensional Ising models with finite-range Interactions (2018) (25)
On the equivalence between KMS-states and equilibrium states for classical systems (1977) (24)
On the ubiquity of the Cauchy distribution in spectral problems (2013) (23)
A comparison of plane rotor and Ising models (1980) (23)
A sufficient condition for the avoidance of sets by measure preserving flows in $\mathbb{R}^n$ (1978) (22)
Bounded Fluctuations and Translation Symmetry Breaking in One-Dimensional Particle Systems (2000) (22)
A Power-Law Upper Bound on the Correlations in the 2D Random Field Ising Model (2018) (21)
Uniqueness of the infinite cluster and related results in percolation (1987) (21)
Proof of Rounding by Quenched Disorder of First Order Transitions in Low-Dimensional Quantum Systems (2011) (21)
Erratum: Proof of the triviality of d4 field theory and some mean-field features of ising models for d>4 (Physical Review Letters (1981) 47, 12 (886)) (1981) (19)
Taylor series expansions for the entropy rate of Hidden Markov Processes (2005) (19)
Fluctuation based proof of the stability of ac spectra of random operators on tree graphs (2005) (19)
Rigorous studies of critical behavior (1986) (18)
Constructive fractional-moment criteria for localization in random operators (2000) (17)
Finite-volume Criteria for Anderson Localization (1999) (16)
Exponential Decay of Correlations in the 2D Random Field Ising Model (2019) (16)
Absence of an intermediate phase for a general class of one-component ferromagnetic models. (1985) (15)
On the Critical Behavior at the Lower Phase Tran- sition of the Contact Process (2006) (14)
Resonances and Partial Delocalization on the Complete Graph (2014) (13)
Time-displaced correlation functions in an infinite one-dimensional mixture of hard rods with different diameters (1978) (13)
Matrix regularizing effects of Gaussian perturbations (2015) (13)
Topological anomalies in the n dependence of the n-states Potts lattice gauge theory (1984) (12)
Instability of phase coexistence and translation invariance in two dimensions (1979) (12)
Persistence under Weak Disorder of AC Spectra of Quasi-Periodic Schroedinger operators on Trees Graphs (2005) (12)
States of one-dimensional Coulomb systems as simple examples of θ vacua and confinement (1981) (11)
Symmetry Breaking in Quasi-1D Coulomb Systems (2010) (10)
Dimerization and Néel Order in Different Quantum Spin Chains Through a Shared Loop Representation (2020) (10)
Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice (2004) (9)
Edge switching transformations of quantum graphs (2017) (8)
On spin systems with quenched randomness: Classical and quantum (2009) (7)
Depinning in the integer-valued Gaussian field and the BKT phase of the 2D Villain model (2021) (7)
On the joint distribution of energy levels of random Schrödinger operators (2008) (7)
Continuum Limits for Critical Percolation and Other Stochastic Geometric Models (1998) (5)
DISORDER-INDUCED DELOCALIZATION ON TREE GRAPHS (2011) (5)
Pfaffian Correlation Functions of Planar Dimer Covers (2016) (5)
Kac–Ward Formula and Its Extension to Order–Disorder Correlators Through a Graph Zeta Function (2017) (4)
Depinning in integer-restricted Gaussian Fields and BKT phases of two-component spin models (2021) (4)
WITHDRAWN: Adiabatic charge transport and the Kubo formula for 2D Hall conductance (2002) (3)
Positive Linear Maps which are Order Bounded on C* Subalgebras (1978) (3)
FRACTIONAL MOMENT METHODS FOR ANDERSON LOCALIZATION IN THE CONTINUUM (2003) (3)
Motional broadening in ensembles with heavy-tail frequency distribution (2011) (3)
Tree Graph Inequalities and Critical Behavior in (1984) (3)
Addendum: ``Some rigorous results on the Sherrington-Kirkpatrick spin glass model'' (1988) (2)
The state of matter : a volume dedicated to E.H. Lieb (1994) (2)
Probabilistic methods for stationary problems of linear transport theory (1979) (2)
Perspectives in Statistical Mechanics (2006) (2)
Momentum distribution in the Tomonaga model at finite temperatures (1974) (2)
Rigorous Results on the Critical Behavior in Statistical Mechanics (1983) (2)
Emergent planarity in two-dimensional Ising models with finite-range Interactions (2019) (1)
Finite-Volume Fractional-Moment Criteria for (2000) (1)
Boosted Simon‐Wolff Spectral Criterion and Resonant Delocalization (2014) (1)
Internal Structure of Coulomb System in One Dimension (1981) (0)
Phase diagrams for regular tree graphs (2015) (0)
Fractional moments from an analytical perspective (2015) (0)
Short Course on the Sherrington Kirkpatrick Model : Lecture 1 (2004) (0)
The eigenvalue point process and a conjectured dichotomy (2015) (0)
Elements of spectral theory (2015) (0)
The relation of Green functions to eigenfunctions (2015) (0)
Emergent Pfaffian Relations in Quasi-Planar Models (2016) (0)
S ep 2 00 7 On the Structure of Quasi-Stationary Competing Particles Systems (2007) (0)
On the ubiquity of the Cauchy distribution in spectral problems (2014) (0)
Communications in Mathematical Physics: Preface (2004) (0)
Density of states bounds: Wegner estimate and Lifshitz tails (2015) (0)
A Power-Law Upper Bound on the Correlations in the 2D Random Field Ising Model (2019) (0)
Anderson localization through path expansions (2015) (0)
On the critical behavior of the surface tension in a random surface model (1985) (0)
Disorder and Localization Phenomena: from Theory to Applications (2008) (0)
Critical Phenomena via Random Walk Representations : Selected Classics and Some Recent Results (2006) (0)
Introduction to the Special Issue in Honor of Joel Lebowitz (2020) (0)
The Journal’s Mission and Standards of Presentation (2004) (0)
Dannie Heineman Prize Talk (2010) (0)
Finite-Volume Fractional-Moment Criteria forAnderson (2000) (0)
The truncated correlations of the Ising model in any dimension decay exponentially fast at all but the critical temperature (2015) (0)
Scientific project : The Ising Model in three and four dimensions (2013) (0)
Diffusion hypothesis and the Green-Kubo-Streda formula (2015) (0)
The Henri Poincaré prize sponsored by the Daniel Iagolnitzer Foundation (2006) (0)
Se p 19 96 On the Number of Incipient Spanning Clusters (2008) (0)
On te structure of quasi-stationary competin particle systems. (2009) (0)
Pfaffian Correlation Functions of Planar Dimer Covers (2017) (0)
Integer quantum Hall effect (2015) (0)
For: The IMA Volumes in Mathematics and its Applications (Springer{Verlag) SCALING LIMIT FOR THE INCIPIENT SPANNING CLUSTERS (1996) (0)
THE CREATION OF SPECTRAL GAPS BY GRAPHDECORATIONJEFFREY (2000) (0)
A geometric perspective on the scaling limits of critical Ising and $\varphi^4_d$ models (2021) (0)
Resonances and Partial Delocalization on the Complete Graph (2014) (0)
Herglotz-Pick functions and their spectra (2015) (0)
Quantum Phases of Cold Bosons in an Optical Lattice (2009) (0)
Stochastic geometry and interacting ﬁelds (2012) (0)
Complete localization in one dimension (2015) (0)
Ergodic operators and their self-averaging properties (2015) (0)
General relations between spectra and dynamics (2015) (0)
Disordered Quantum Many-Body Systems (2014) (0)
Disorder Effects on Quantum and Classical 1 st Order Phase Transitions (2012) (0)
Constructive criteria for Anderson localization (2015) (0)
Localization at high disorder and at extreme energies (2015) (0)
Random Currents and Continuity of Ising Model’s Spontaneous Magnetization (2014) (0)
Kac–Ward Formula and Its Extension to Order–Disorder Correlators Through a Graph Zeta Function (2018) (0)
Constructive Fractional-Moment Criteria forLocalization in Random (2007) (0)
Dynamical localization and fractional moment criteria (2015) (0)
On extensions of flows in the presence of sets of singularities (1978) (0)
Ruminations on matrix convexity and the strong subadditivity of quantum entropy (2022) (0)
Strategies for mapping exponential decay (2015) (0)

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