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Lectures on the random field ising m...

Rychkov, Slava.

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Lectures on the random field ising model = from parisi-sourlas supersymmetry to dimensional reduction /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lectures on the random field ising model/ by Slava Rychkov.
Reminder of title:	from parisi-sourlas supersymmetry to dimensional reduction /
Author:	Rychkov, Slava.
Published:	Cham :Springer Nature Switzerland : : 2023.,
Description:	ix, 64 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Field theory (Physics) - Mathematical models. -
Online resource:	https://doi.org/10.1007/978-3-031-42000-9
ISBN:	9783031420009

Lectures on the random field ising model = from parisi-sourlas supersymmetry to dimensional reduction /
Rychkov, Slava.

Lectures on the random field ising modelfrom parisi-sourlas supersymmetry to dimensional reduction /[electronic resource] :by Slava Rychkov. - Cham :Springer Nature Switzerland :2023. - ix, 64 p. :ill., digital ;24 cm. - SpringerBriefs in physics,2191-5431. - SpringerBriefs in physics..

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.

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.

ISBN: 9783031420009

Standard No.: 10.1007/978-3-031-42000-9doiSubjects--Topical Terms:

3632316
Field theory (Physics)
--Mathematical models.

LC Class. No.: QC173.7

Dewey Class. No.: 530.14

Lectures on the random field ising model = from parisi-sourlas supersymmetry to dimensional reduction /
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100 1 $a Rychkov, Slava. $3 3217207
245 1 0 $a Lectures on the random field ising model $h [electronic resource] : $b from parisi-sourlas supersymmetry to dimensional reduction / $c by Slava Rychkov.
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300 $a ix, 64 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in physics, $x 2191-5431
505 0 $a 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.
520 $a 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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