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Set Theory, Model Theory and Applications

אפר 22—26, 2018, Eilat Campus of Ben-Gurion University of the Negev (Israel)

BGU Probability and Ergodic Theory (PET) seminar

A power-law upper bound on the decay of correlations in the two-dimensional random-field Ising model

אפר 24, 11:00—12:00, 2018, 201

מרצה

Ron Peled (Tel Aviv University)

תקציר

The random-field Ising model (RFIM) is a standard model for a disordered magnetic system, obtained by placing the standard ferromagnetic Ising model in a random external magnetic field. Imry-Ma (1975) predicted, and Aizenman-Wehr (1989) proved, that the two-dimensional RFIM has a unique Gibbs state at any positive intensity of the random field and at all temperatures. Thus, the addition of an arbitrarily weak random field suffices to destroy the famed phase transition of the two-dimensional Ising model. We study quantitative features of this phenomenon, bounding the decay rate of the effect of boundary conditions on the magnetization in fi nite systems. This is known to decay exponentially fast for a strong random fi eld. The main new result is a power-law upper bound which is valid at all field strengths and at all temperatures, including zero. Our analysis proceeds through a streamlined and quantified version of the Aizenman-Wehr proof. Several open problems will be mentioned. Joint work with Michael Aizenman.

צוהר למחקר

אנתרופיה, אינפורמציה, סיבוכיות ואי סדר במערכות דינאמיות

אפר 24, 16:15—18:00, 2018, -101

מרצה

תם מאירוביץ


תאריכים אחרים