Research Articles

Recent works are available on arXive (Aizenman in Math. and Phys.)
Research articles (Book and Reviews  are listed separately)

• Michael Aizenman, Hugo Duminil-Copin, Simone Warzel, "Dimerization and Néel order in different quantum spin chains through a shared loop representation'',  arXiv:2002.02543 (2020 preprint).

• Michael Aizenman, Hugo Duminil-Copin, "Marginal triviality of the scaling limits of critical 4D Ising and φ44 models'', arXiv:1912.07973 (2019 preprint).

• Michael Aizenman, Matan Harel, Ron Peled, "Exponential decay of correlations in the 2D random field Ising model'',  arXiv:1907.06459 (2019 preprint).

• Michael Aizenman, Ron Peled,  "A power-law upper bound on the correlations in the 2D random field Ising model", Comm. Math. Phys. 372, 865-892 (2019)

• Michael Aizenman, Hugo Duminil-Copin, Vincent Tassion, Simone Warzel, "Emergent Planarity in two-dimensional Ising Models with finite-range Interactions'', Invent. Math. 216, 661 (2019)  

• Michael Aizenman, Holger Schanz, Uzy Smilansky, Simone Warzel,  "Edge switching transformations of quantum graphs'', Acta Physica Polonica A 132, 1699-1703 (2017).

• Michael Aizenman, Simone Warzel, "Kac-Ward formula and its extension to order-disorder correlators through a graph zeta function'', J. Stat. Phys. 173, 1755–1778 (2018).

• Michael Aizenman, Manuel Laínz Valcázar, Simone Warzel, "Pfaffian Correlation Functions of Planar Dimer Covers'',  J. Stat. Phys. 166: 1078-1091 (2017).

• Michael Aizenman, Ron Peled, Jeffrey Schenker, Mira Shamis, Sasha Sodin, "Matrix regularizing effects of Gaussian perturbations'', Comm. Contemp. Math.  19, 1750028 (2017).

• Michael Aizenman, Simone Warzel, "Boosted Simon-Wolff Spectral Criterion and Resonant Delocalization", Commun. Pure Appl. Math. B, 2195-2218 (2016). 

• Michael Aizenman, Mira Shamis, Simone Warzel, "Resonances and partial delocalization on the complete graph'', Ann. Henri Poincaré 16, 1969-2003 (2015). 

• Michael Aizenman, Simone Warzel, "On the ubiquity of the Cauchy distribution in spectral problems'', Probab. Theory Relat. Fields 163, 61-87 (2015).

• Michael Aizenman, Hugo Duminil-Copin, Vladas Sidoravicius, "Random Currents and Continuity of Ising Model's Spontaneous Magnetization", Comm. Math. Phys.,  334, 719 (2015).

· M. Aizenman and S. Warzel "Resonant delocalization for random Schrödinger operators on tree graphs". 
J. Eur. Math. Soc. 15 , 1167-1222 (2013).

· M. Aizenman and S. Warzel,  "Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs".  J. Math. Phys. 53, 095205 (2012).

· M. Aizenman, 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).

· M. Aizenman and S. Warzel, "Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder". Euro. Phys. Lett. 96, 37004 (2011).

· M. Aizenman and S. S. Warzel, "Extended States in a Lifshits Tail Regime for Random Schrödinger Operators on Trees". Phys. Rev. Lett. 106, 136801 (2011).

· Y. Sagi, R. Pugatch, I. Almog, N. Davidson and M. Aizenman,  "Motional broadening in ensembles with heavy-tail frequency distribution. Phys. Rev. A 83, 043821 (2011).

· M. Aizenman, S. Jansen, and P. Jung, "Symmetry breaking in quasi-1D Coulomb systems". Ann. Henri Poincaré 11, 1453 (2010).

· M. Aizenman, R.L. Greenblatt, and J.L. Lebowitz, "On Spin Systems with Quenched Randomness: Classical and Quantum". Physica A 389 , 2902 (2010).

· R.L. Greenblatt, M. Aizenman, J.L. Lebowitz, "Rounding of First Order Transitions in Low-Dimensional Quantum Systems with Quenched Disorder". Phys. Rev. Lett. 103, 197201 (2009).

· M. Aizenman and S. Warzel, "Localization Bounds for Multiparticle Systems". Comm. Math. Phys. 290, 903 (2009).

· M. Aizenman and S. Warzel, "On the Joint Distribution of Energy Levels of Random Schrödinger Operators. J. Phys. A: Math. Theor. 42, 045201 (2009).

· M. Aizenman and L-P Arguin, "On the Structure of Quasi-Stationary Competing Particles Systems".  Ann. Prob. 27 , 1080 (2009).

· M. Aizenman, 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).

· M. Aizenman and 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).

· M. Aizenman and S. Warzel, "The Canopy Graph and Level Statistics for Random Operators on Trees". Math. Phys. Anal. Geom. (MPAG), 9, 291 (2006 [app. 2007]).

· M. Aizenman, 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).

· M. Aizenman, 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]).

· M. Aizenman, R. Sims and S. Warzel, "Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder". Comm. Math. Phys. 264, 371 (2006).

· M. Aizenman, 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).

· M. Aizenman, A. Elgart, S. Naboko, G. Stoltz, and J.H. Schenker, "Moment Analysis for Localization in Random Schrödinger Operators". Inventiones Mathematicae 163, 343 (2006).

· A. Ruzmaikina, M. Aizenman, "Characterization of Invariant Measures at the Leading Edge for Competing Particle Systems". Ann. Probab., 33, 82, (2005).

· M. Aizenman, 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).

· M. Aizenman, R. Sims, and S.L. Starr, Extended variational principle for the Sherrington-Kirkpatrick spin-glass model. Phys. Rev. B 68, 214403 (2003).

· M. Aizenman, J.H. Schenker, R.M. Friedrich, and D. Hundertmark, "Finite-Volume Fractional-Moment Criteria for Anderson Localization". Comm. Math. Phys. 224, 219 (2001).

· M. Aizenman, S. Goldstein and J.L. Lebowitz, "Bounded Fluctuations and Translation Symmetry Breaking in One-dimensional Particle Systems. J. Stat. Phys. 103, 601 (2001).

· M. Aizenman, J.H. Schenker, "The creation of Spectral gaps by Graph Decorations". Lett. Math. Phys. 53, 253 (2000).

· M. Aizenman, J.H. Schenker, R.M. Friedrich, and D. Hundertmark, "Constructive Fractional-moment Criteria for Localization in Random Operators. Physica A. 279, 369 (2000).

· M. Aizenman, B. Duplantier and A. Aharony, "Connectivity Exponents and External Perimeter in 2D Independent Percolation Models". Phys. Rev. Lett. 83, 1359 (1999).

· M. Aizenman, A. Burchard, C.M. Newman, D.B. Wilson, "Scaling Limits for Minimal and Random Sanning Trees in Two Dimensions". Rand. Struct. Alg. 15, 319 (1999).

· M. Aizenman,  A. Burchard, "Hölder Regularity and Dimension Bounds for Random Curves". Duke Math. J. 99, 419 (1999).

· M. Aizenman, P. Contucci, "Stability of the Quenched State in Mean Field Spin Glass Models".  J. Stat. Phys. 92, 765 (1998).

· M. Aizenman, G.M. Graf,  "Localization Bounds for an Electron Gas". J. Phys. A: Math. Gen. 31, 6783 (1998).

· M. Aizenman, "On the Number of Incipient Spanning Clusters". Nuclear Physics B [FS] 485, 551 (1997).

· M. Aizenman, "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).

· M. Aizenman, "Localization at Weak Disorder: Some Elementary Bounds". Rev. Math. Phys. 6, 1163 (1994).

· M. Aizenman, B. Nachtergaele, "Geometric Aspects of Quantum Spin States. Comm. Math. Phys. 164, 17 (1994).

· M. Aizenman, S. Molchanov, "Localization at Large Disorder and at Extreme Energies: an Elementary Derivation". Comm. Math. Phys. 157, 245 (1993).

· M. Aizenman,  G. Grimmett, "Strict Monotonicity of Critical Points in Percolation and Ferromagnetic Models. J. Stat. Phys., 63, 817 (1991).

·  D. Barsky and M. Aizenman, "Percolation Critical Exponents Under the Triangle Condition". Ann. Prob. 13, 1520 (1991).

· M. Aizenman, E. H. Lieb, "Magnetic Properties of Some Itinerant Electron Systems at T > 0. Phys. Rev. Lett., 65, 1470-1473 (1990).

· M. Aizenman,  J. Wehr, "Rounding Effects of Quenched Randomness on First-Order Phase Transitions". Comm. Math. Phys. 130, 489 (1990).

· M. Aizenman,  J. Wehr, "Fluctuations of Extensive Functions of Quenched Random Couplings". J. Stat. Phys. 60, 287 (1990).

· M. Aizenman,  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).

· M. Aizenman,  J. Lebowitz, "Metastability in Bootstrap Percolation". J. Phys. A: Math. Gen. 21, 3801 (1988).

· M. Aizenman,  R. Fernández, "Critical Exponents for Long-Range Interactions". Lett. Math. Phys. 16, 39 (1988).

· M. Aizenman,  J. Bricmont and J. L. Lebowitz, "Percolation of the Minority Spins in High-Dimensional Ising Models". J. Stat. Phys., 49 859, (1987).

· M. Aizenman,  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).

· M. Aizenman, 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).

· M. Aizenman,  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).

· M. Aizenman,  "Rigorous Studies of Critical Behavior. Physica", 140 A, 225 (1986).

· M. Aizenman, D. Barsky and R. Fernández, "The Phase Transition in a General Class of Ising-Type Models is Sharp". J. State. Phys. 47, 343 (1987).

· M. Aizenman, 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).

· M. Aizenman, D. Barsky, "Sharpness of the Phase Transition in Percolation Models". Comm. Math. Phys., 108, 489 (1987).

· M. Aizenman, 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).

· M. Aizenman, C. Newman, "Discontinuity of the Percolation Density in One Dimensional 1/(x-y)2 Percolation Models". Comm. Math. Phys., 107, 611 (1986).

· M. Aizenman, R. Fernández, "On the Critical Behavior of the Magnetization in High-Dimensional Ising Models". J. Stat. Phys., 44, 383 (1986).

· M. Aizenman, M. Harn, "On the Vanishing of the Surface Tension in a Random Surface Model". Nucl. Phys., B 257 [FS 14], 859 (1985).

· M. Aizenman, "Absence of an Intermediate Phase in a General Class of One Component Ferromagnetic Systems". Phys. Rev. Lett., 54, 839 (1985).

· M. Aizenman, "Self Intersection of Brownian Paths as a Case Study of a Renormalization Group Method for Quantum Field Theory". Comm. Math. Phys., 97, 91 (1985).

· M. Aizenman, J. Fröhlich, "Topological Anomalies in the n-Dependence of the n-States Potts Lattice Gauge Theory". Nucl. Phys., B 235 [FS 11], 1 (1984).

· M. Aizenman, C. Newman, "Tree Graph Inequalities and Critical Behavior in Percolation Models. J. Stat. Phys., 36, 107 (1984).

· M. Aizenman,  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).

· M. Aizenman, R. Graham, "On the Renormalized Coupling Constant and the Susceptibility in φ4 Field Theory and the Ising Model in Four Dimensions". Nucl. Phys., B 255 [FS9], 261 (1983).

· M. Aizenman, B. Simon, "Brownian Motion and Harnack Inequality for Schrödinger Operators". Commun. Pure and Appl. Math., 35, 209 (1982).

· M. Aizenman, "Geometric Analysis of φ4Fields and Ising Models". Comm. Math. Phys., 86, 1 (1982).

·  M. Aizenman, "Proof of the Triviality of φ4 Field Theory and Some Mean-Field Features of Ising Models for d > 4". Phys. Rev. Let., 47, 1 (1981).

· M. Aizenman, E. H. Lieb, "The III-rd Law of Thermodynamics and the Degeneracy of Ground States in Lattice Systems". J. Stat. Phys., 24, 279 (1981).

· M. Aizenman, J. Fröhlich, "States of One-Dimensional Coulomb Systems as Simple Examples of θ -vacua and Confinement". J. Stat. Phys., 26, 347 (1981).

· M. Aizenman, P. A. Martin, "Structure of Gibbs States of One Dimensional Coulomb Systems". Comm. Math. Phys., 78, 99 (1980).

· M. Aizenman, B. Simon, "Local Ward Identities and the Decay of Correlations in Ferromagnets". Comm. Math. Phys., 77, 137 (1980).

· M. Aizenman, B. Simon, "A Comparison of Plane Rotor and Ising Models". Phys. Lett., 76A, 281 (1980).

· M. Aizenman, F. Delyon and B. Souillard, "Lower Bounds on the Cluster Size Distribution". J. Stat. Phys., 23 267 (1980).

· M. Aizenman, H. Spohn, "Probabilistic Methods for Stationary Problems of Linear Transport Theory". J. Stat. Phys., 21, 23 (1979).

· M. Aizenman, T. A. Bak, "Convergence to Equilibrium in a System of Reacting Polymers". Comm. Math. Phys., 65, 203 (1979).

· M. Aizenman, "Translation Invariance and Instability of Phase Coexistence in the Two Dimensional Ising System". Comm. Math. Phys., 73, 83 (1980).

· M. Aizenman,  "Instability of Phase Coexistence and Translation Invariance in Two Dimensions". Phys. Rev. Lett., 43, 407 (1979).

· M. Aizenman, 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).

· M. Aizenman, E. H. Lieb, "On Semi-Classical Bounds for Eigenvalues of Schrödinger Operators". Phys. Lett., 66A, 427 1978.

· M. Aizenman, "A Sufficient Condition for the Avoidance of Sets by Measure Preserving Flows in Rn". Duke Journal of Math., 45 809, (1978).

· M. Aizenman, "On Vector Fields as Generators of Flows: A Counterexample to Nelson's Conjecture". Annals of Math. 107, 287 (1978).

· M. Aizenman,  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).

· M. Aizenman, E. B. Davies and E. H. Lieb, "Positive Linear Maps Which are Order Bounded on C* Subalgebras". Adv. in Math., 28, 84 (1978).

· M. Aizenman, 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).

· M. Aizenman, G. Gallavotti, S. Goldstein and J. L. Lebowitz,  "Stability and Equilibrium States of Infinite Classical Systems". Comm. Math. Phys., 48, 1 (1976).

· M. Aizenman, J. L. Lebowitz and S. Goldstein, "On the Stability of Equilibrium States of Finite Classical Systems". J. Math. Phys., 16, 1284 (1975).

· M. Aizenman, S. Goldstein and J. L. Lebowitz,  "Ergodic Properties of an Infinite One Dimensional Hard Rod System". Comm. Math. Phys., 39, 288 (1975).

· M. Aizenman, H. Gutfreund, "Momentum Distribution in the Tomonaga Model at Finite Temperatures". J. Math. Phys., 15, 643 (1974).

(Conference Proceedings are listed separately)