EAN: 9783031419997

SPRINGERBRIEFS IN PHYSICS LECTURES ON THE RAN...

This book is about the Random Field Ising Model (RFIM) - a paradigmatic spin model featuring a
frozen disordering field. The focus is on the second-order phase transition between the
paramagnetic and ferromagnetic phases  and the associated critical exponents. The book starts
by summarizing the current knowledge about the RFIM from experiments  numerical simulations and
rigorous mathematical results. It then reviews the classic theoretical works from the 1970's
which suggested a property of dimensional reduction - that the RFIM critical exponents should
be the same as for the ordinary  non-disordered  Ising model of lower dimensionality  and
related this an emergent Parisi-Sourlas supersymmetry. As is now known  these remarkable
properties only hold when the spatial dimensionality of the model is larger than a critical
dimension. The book presents a method to estimate the critical dimension  using standard tools
such as the replica trick and perturbative renormalization group  whose result is in agreement
with the numerical simulations. Some more elementary steps in the derivations are left as
exercises for the readers. This book is of interest to researchers  PhD students and advanced
master students specializing in statistical field theory.

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