Michael Aizenman   

Professor of Physics and Mathematics
Princeton University



Homepage | Research Articles | Conf. Proceedings | Curriculum Vitae

PDF fies of recent works are available at:   arXive (search Aizenman, check Math. and Phys.)



Preprints  

  • (With S. Warzel) Resonant delocalization for random Schrödinger operators on tree graphs.
    (http://arxiv.org/abs/1104.0969, to appear in JEMS (J. Europ. Math. Soc.))

  • Articles in refereed journals   (Conf. Proceedings / Reviews are listed separately)

  • (With R.L. Greenblatt, and J.L. Lebowitz) Proof of Rounding by Quenched Disorder of First Order Transitions in Low-Dimensional Quantum Systems. J. Math. Phys. 53, 023301 (2012).
  • (With S. Warzel) Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder. Euro. Phys. Lett. 96, 37004 (2011).
  • (With S. Warzel) Extended States in a Lifshits Tail Regime for Random Schrödinger Operators on Trees. Phys. Rev. Lett. 106, 136801 (2011).
  • (With Y. Sagi, R. Pugatch, I. Almog and N. Davidson) Motional broadening in ensembles with heavy-tail frequency distribution. Phys. Rev. A 83, 043821 (2011).
  • (With S. Jansen, and P. Jung) Symmetry breaking in quasi-1D Coulomb systems. Ann. Henri Poincaré 11, 1453 (2010).
  • (With R.L. Greenblatt, and J.L. Lebowitz) On Spin Systems with Quenched Randomness: Classical and Quantum. Physica A 389 , 2902 (2010).
  • (With R.L. Greenblatt, and J.L. Lebowitz) Rounding of First Order Transitions in Low-Dimensional Quantum Systems with Quenched Disorder. Phys. Rev. Lett. 103, 197201 (2009).
  • (with S. Warzel) Localization Bounds for Multiparticle Systems. Comm. Math. Phys. 290, 903 (2009).
  • (with S. Warzel) On the Joint Distribution of Energy Levels of Random Schrödinger Operators. J. Phys. A: Math. Theor. 42, 045201 (2009).
  • (with L-P Arguin) On the Structure of Quasi-Stationary Competing Particles Systems.
    Ann. Prob. 27 , 1080 (2009).
  • (with F. Germinet, A. Klein, and S. Warzel) On Bernoulli Decompositions for Random Variables, Concentration Bounds, and Spectral Localization.
    Prob. Th. Rel. Fields. (PTRF) 143 , 219 (2009).
  • (with P. Jung) On the Critical Behavior at the Lower Phase Transition of the Contact Process. Latin American Jour. Prob. and Math. Stat. (ALEA). 3, 301 (2007).
  • (with S. Warzel) The Canopy Graph and Level Statistics for Random Operators on Trees.
    Math. Phys. Anal. Geom. (MPAG), 9, 291 (2006 [app. 2007]).
  • (with O. Zuk, E. Domany, and I. Kanter) From Finite-System Entropy to Entropy Rate for a Hidden Markov Process. IEEE Signal Processing Letters 13,517 (2006).
  • (with S. Warzel) Persistence Under Weak Disorder of AC Spectra of Quasi-Periodic Schroedinger Operators on Trees Graphs. Moscow Math. J. 5, 499 (2005 [app. 2006]).
  • (with R. Sims and S. Warzel) Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder. Comm. Math. Phys. 264, 371 (2006).
  • (with R. Sims and S. Warzel) Stability of the Absolutely Continuous Spectrum of Random Schroedinger Operators on Tree Graphs. Prob. Th. Rel. Fields, 136, 363 (2006).
  • (with A. Elgart, S. Naboko, G. Stoltz, and J.H. Schenker) Moment Analysis for Localization in Random Schrödinger Operators. Inventiones Mathematicae 163, 343 (2006).
  • (with A. Ruzmaikina) Characterization of Invariant Measures at the Leading Edge for Competing Particle Systems. Ann. Probab., 33, 82, (2005).
  • (with E.H. Lieb, R. Seiringer, J.P. Solovej, and J. Yngvason) Bose-Einstein Quantum Phase Transition in an Optical Lattice Model. Phys. Rev. A 70, 023612 (2004).
  • (with R. Sims, and S.L. Starr) Extended variational principle for the Sherrington-Kirkpatrick spin-glass model. Phys. Rev. B 68, 214403 (2003).
  • (with J.H. Schenker, R.M. Friedrich, and D. Hundertmark) Finite-Volume Fractional-Moment Criteria for Anderson Localization. Comm. Math. Phys. 224, 219 (2001).
  • (with S. Goldstein and J.L. Lebowitz) Bounded Fluctuations and Translation Symmetry Breaking in One-dimensional Particle Systems. J. Stat. Phys. 103, 601 (2001).
  • (with J.H. Schenker) The creation of Spectral gaps by Graph Decorations. Lett. Math. Phys. 53, 253 (2000).
  • (with J.H. Schenker, R.M. Friedrich, and D. Hundertmark) Constructive Fractional-moment Criteria for Localization in Random Operators. Physica A. 279, 369 (2000).
  • (with A. Aharony and B. Duplantier) Connectivity Exponents and External Perimeter in 2D Independent Percolation Models. Phys. Rev. Lett. 83, 1359 (1999).
  • (with A. Burchard, C.M. Newman and D.B. Wilson) Scaling Limits for Minimal and Random Spanning Trees in Two Dimensions. Rand. Struct. Alg. 15, 319 (1999).
  • (with A. Burchard) Hölder Regularity and Dimension Bounds for Random Curves. Duke Math. J. 99, 419 (1999).
  • (with P. Contucci) Stability of the Quenched State in Mean Field Spin Glass Models. J. Stat. Phys. 92, 765 (1998).
  • (with G.M. Graf) Localization Bounds for an Electron Gas. J. Phys. A: Math. Gen. 31, 6783 (1998).
  • On the Number of Incipient Spanning Clusters. Nuclear Physics B [FS] 485, 551 (1997).
  • On the Slow Decay of O(2) Correlations in the Absence of Topological Excitations; remark on the Patrascioiu-Seiler model. J. Stat. Phys. 77, 351 (1994).
  • Localization at Weak Disorder: Some Elementary Bounds. Rev. Math. Phys. 6, 1163 (1994).
  • (with B. Nachtergaele) Geometric Aspects of Quantum Spin States. Comm. Math. Phys. 164, 17 (1994).
  • (with S. Molchanov) Localization at Large Disorder and at Extreme Energies: an Elementary Derivation. Comm. Math. Phys. 157, 245 (1993).
  • (with G. Grimmett) Strict Monotonicity of Critical Points in Percolation and Ferromagnetic Models. J. Stat. Phys., 63, 817 (1991).
  • (with D. Barsky) Percolation Critical Exponents Under the Triangle Condition. Ann. Prob. 13, 1520 (1991).
  • (with E. H. Lieb) Magnetic Properties of Some Itinerant Electron Systems at T > 0. Phys. Rev. Lett., 65, 1470-1473 (1990).
  • (with J. Wehr) Rounding Effects of Quenched Randomness on First-Order Phase Transitions. Comm. Math. Phys. 130, 489 (1990).
  • (with J. Wehr) Fluctuations of Extensive Functions of Quenched Random Couplings. J. Stat. Phys. 60, 287 (1990).
  • (with J. Wehr) Rounding of First-Order Phase Transitions in Systems with Quenched Disorder. Phys. Rev. Lett., 62, 2503 (1989). Erratum: PRL, 64, 1311 (E) (1990).
  • (with J. Lebowitz) Metastability in Bootstrap Percolation. J. Phys. A: Math. Gen. 21, 3801 (1988).
  • (with R. Fernández) Critical Exponents for Long-Range Interactions. Lett. Math. Phys. 16, 39 (1988).
  • (with J. Bricmont and J. L. Lebowitz) Percolation of the Minority Spins in High-Dimensional Ising Models. J. Stat. Phys., 49 859, (1987).
  • (with J. T. Chayes, L. Chayes and C. Newman) Discontinuity of the Order Parameter in One Dimensional 1/(x-y)^2 Ising and Potts Models. J. Stat. Phys., 50 1, (1988).
  • (with D. Ruelle and J. L. Lebowitz) Some Rigorous Results on the Sherrington-Kirkpatrik Spin Glass Model. Comm. Math. Phys., 112 3, (1987). Addendum: CMP 116 527 (1988).
  • (with J. T. Chayes, L. Chayes and C. Newman) The Phase Boundary in Dilute and Random Ising and Potts Ferromagnets. J. Phys. A: Math. Gen., 20, L 313 (1987).
  • Rigorous Studies of Critical Behavior. Physica, 140 A, 225 (1986).
  • (with D. Barsky and R. Fernández) The Phase Transition in a General Class of Ising-Type Models is Sharp. J. State. Phys. 47, 343 (1987).
  • (with H. Kesten and C. Newman) Uniqueness of the Infinite Cluster and Continuity of Connectivity Functions for Short and Long Range Percolation. Comm. Math. Phys., 111, 505 (1987).
  • (with D. Barsky) Sharpness of the Phase Transition in Percolation Models. Comm. Math. Phys., 108, 489 (1987).
  • (with R. Holley) Rapid Convergence to Equilibrium of Stochastic Ising Models in the Dobrushin Shlosman Regime. In: Percolation Theory and Ergodic Theory of Infinite Particle Systems (The IMA Volumes in Math. and Its Applic.; v. 8), H. Kesten, (ed.). Springer-Verlag, (1987).
  • (with C. Newman) Discontinuity of the Percolation Density in One Dimensional 1/(x-y)^2 Percolation Models. Comm. Math. Phys., 107, 611 (1986).
  • (with R. Fernández) On the Critical Behavior of the Magnetization in High-Dimensional Ising Models. J. Stat. Phys., 44, 383 (1986).
  • (with M. Harn) On the Vanishing of the Surface Tension in a Random Surface Model. Nucl. Phys., B 257 [FS 14], 859 (1985).
  • Absence of an Intermediate Phase in a General Class of One Component Ferromagnetic Systems. Phys. Rev. Lett., 54, 839 (1985).
  • Self Intersection of Brownian Paths as a Case Study of a Renormalization Group Method for Quantum Field Theory. Comm. Math. Phys., 97, 91 (1985).
  • (with J. Fröhlich) Topological Anomalies in the n-Dependence of the n-States Potts Lattice Gauge Theory. Nucl. Phys., B 235 [FS 11], 1 (1984).
  • (with C. Newman) Tree Graph Inequalities and Critical Behavior in Percolation Models. J. Stat. Phys., 36, 107 (1984).
  • (with J. T. Chayes, L. Chayes, J. Fröhlich and L. Russo) On a Sharp Transition from Area Law to a Perimeter Law in a System of Random Surfaces. Comm. Math. Phys., 92, 19 (1983).
  • (with R. Graham) On the Renormalized Coupling Constant and the Susceptibility in φ^4 Field Theory and the Ising Model in Four Dimensions. Nucl. Phys., B 255 [FS9], 261 (1983).
  • (with B. Simon) Brownian Motion and Harnack Inequality for Schrödinger Operators. Commun. Pure and Appl. Math., 35, 209 (1982).
  • Geometric Analysis of φ^4 Fields and Ising Models. Comm. Math. Phys., 86, 1 (1982).
  • Proof of the Triviality of φ^4 Field Theory and Some Mean-Field Features of Ising Models for d > 4. Phys. Rev. Let., 47, 1 (1981).
  • (with E. H. Lieb) The III-rd Law of Thermodynamics and the Degeneracy of Ground States in Lattice Systems. J. Stat. Phys., 24, 279 (1981).
  • (with J. Fröhlich) States of One-Dimensional Coulomb Systems as Simple Examples of θ -vacua and Confinement. J. Stat. Phys., 26, 347 (1981).
  • (with P. A. Martin) Structure of Gibbs States of One Dimensional Coulomb Systems. Comm. Math. Phys., 78, 99 (1980).
  • (with B. Simon) Local Ward Identities and the Decay of Correlations in Ferromagnets. Comm. Math. Phys., 77, 137 (1980).
  • (with B. Simon) A Comparison of Plane Rotor and Ising Models. Phys. Lett., 76A, 281 (1980).
  • (with F. Delyon and B. Souillard) Lower Bounds on the Cluster Size Distribution. J. Stat. Phys., 23 267 (1980).
  • (with H. Spohn) Probabilistic Methods for Stationary Problems of Linear Transport Theory. J. Stat. Phys., 21, 23 (1979).
  • (with T. A. Bak) Convergence to Equilibrium in a System of Reacting Polymers. Comm. Math. Phys., 65, 203 (1979).
  • Translation Invariance and Instability of Phase Coexistence in the Two Dimensional Ising System. Comm. Math. Phys., 73, 83 (1980).
  • Instability of Phase Coexistence and Translation Invariance in Two Dimensions. Phys. Rev. Lett., 43, 407 (1979).
  • (with S. Goldstein and J. L. Lebowitz) Conditional Equilibrium and the Equivalence of Microcanonical and Grand Canonical Ensembles in the Thermodynamic Limit. Comm. Math. Phys., 62, 279 (1978).
  • (with E. H. Lieb) On Semi-Classical Bounds for Eigenvalues of Schrödinger Operators. Phys. Lett., 66A, 427 1978.
  • A Sufficient Condition for the Avoidance of Sets by Measure Preserving Flows in R^n. Duke Journal of Math., 45 809, (1978).
  • On Vector Fields as Generators of Flows: A Counterexample to Nelson's Conjecture. Annals of Math. 107, 287 (1978).
  • (with J. L. Lebowitz and J. Marro) Time Displaced Correlation Functions in an Infinite One Dimensional Mixture of Hard Rods with Different Diameters. J. Stat. Phys., 18, 287 (1978).
  • (with E. B. Davies and E. H. Lieb) Positive Linear Maps Which are Order Bounded on C* Subalgebras. Adv. in Math., 28, 84 (1978).
  • (with S. Goldstein, C. Gruber, J. L. Lebowitz and P. Martin) On the Equivalence Between KMS-States and Equilibrium States for Classical Systems. Comm. Math. Phys., 53, 209 (1977).
  • (with G. Gallavotti, S. Goldstein and J. L. Lebowitz) Stability and Equilibrium States of Infinite Classical Systems. Comm. Math. Phys., 48, 1 (1976).
  • (with J. L. Lebowitz and S. Goldstein) On the Stability of Equilibrium States of Finite Classical Systems. J. Math. Phys., 16, 1284 (1975).
  • (with S. Goldstein and J. L. Lebowitz) Ergodic Properties of an Infinite One Dimensional Hard Rod System. Comm. Math. Phys., 39, 288 (1975).
  • (with H. Gutfreund) Momentum Distribution in the Tomonaga Model at Finite Temperatures. J. Math. Phys., 15, 643 (1974).


  • Note: Conference Proceedings are listed separately (see Conf. Proceedings / Reviews).


    Last updated:  4/25/2008


      Research supported by NSF.     Current Grant: DMS-0602360.