Lectures on the random field ising model : from Parisi-Sourlas supersymmetry to dimensional reduction / Slava Rychkov.
Rychkov, Slava, author.
2023
QC173.7
Available Online

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Title Lectures on the random field ising model : from Parisi-Sourlas supersymmetry to dimensional reduction / Slava Rychkov.
Author Rychkov, Slava, author.
ISBN 9783031420009 (electronic bk.)
3031420004 (electronic bk.)
9783031419997
3031419995
DOI https://doi.org/10.1007/978-3-031-42000-9
Published Cham : Springer, 2023.
Language English
Description 1 online resource (ix, 64 pages) : illustrations.
Item Number 10.1007/978-3-031-42000-9 doi
Call Number QC173.7
Dewey Decimal Classification 530.14
Summary 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.
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed September 18, 2023).
Series SpringerBriefs in physics, 2191-5431
Available in Other Form Lectures on the Random Field Ising Model
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Record Appears in Online Resources > Ebooks
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1 History, Basics, Experiments and Simulations
2 Parisi-Sourlas theory, dimensional reduction
3 Replicas, Cardy transform, leaders, loss of SUSY
4 Open problems and future directions.

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