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Lectures on the Random Field Ising Model: From Parisi-Sourlas Supersymmetry to Dimensional Reduction (SpringerBriefs in Physics) free ebook download

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Author(s):	Slava Rychkov

Date:	2024	Format:	rar	Language:	English	ISBN/ASIN:	3031419995
Pages:	73	OCR:		Quality:		ISBN13:
Uploader:	gestalt	Upload Date:	11/25/2023 1:59:07 AM

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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 1970s 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.
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Tags: Dimensional Field Ising Lectures Model Parisi-Sourlas Random Reduction SpringerBriefs Supersymmetry

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Lectures on the Random Field Ising Model: From Parisi-Sourlas Supersymmetry to Dimensional Reduction (SpringerBriefs in Physics) free ebook download

Category: Physics

Description: Click to see full description

Category:
Physics