Abstract
We show that, for α > 1 ∕ 2 and as soon as β > 0, disorder is relevant, in the sense that the critical behavior of the disordered system differs from the one of the pure, i.e. homogeneous, system. We do this by establishing a smoothing inequality for the free energy. We then review the literature on the effect of the disorder on phase transitions. In doing so we will present a number of physical predictions on disordered Ising models that are challenges for mathematicians.
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Giacomin, G. (2011). Relevant Disorder Estimates: The Smoothing Phenomenon. In: Disorder and Critical Phenomena Through Basic Probability Models. Lecture Notes in Mathematics(), vol 2025. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21156-0_5
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DOI: https://doi.org/10.1007/978-3-642-21156-0_5
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