Event

Michael Aizenman, Princeton University

Thursday, September 27, 2018 16:00to17:00
Room 1140, Pav. André-Aisenstadt, CA

The Imry-Ma effect and the decay of correlations under quenched random field

The famed discontinuity of the magnetization in the two dimensional Ising model is unstable to the addition of quenched random magnetic field of uniform variance, even if that is small. The talk will focus on a quantitative version of the statement established in a previous work with J. Wehr. The result is a power-law upper bound on the decay of the effects of boundary conditions on the magnetization in finite systems, as function of the distance to the boundary. The analysis applies to all field strengths and all temperatures, including T =0. However the result does not resolve the question of possible transition to exponential decay at weak disorder. The corresponding questions concerning disorder effects on systems with continuous symmetry in three and four dimensions also remain open. The talk is based on a recent joint work with Ron Peled (TAU).
 

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