LEADER 03284nam 22005775 450 001 9910746090403321 005 20230907165133.0 010 $a3-031-42000-4 024 7 $a10.1007/978-3-031-42000-9 035 $a(MiAaPQ)EBC30736071 035 $a(CKB)28162819000041 035 $a(Au-PeEL)EBL30736071 035 $a(DE-He213)978-3-031-42000-9 035 $a(PPN)272736317 035 $a(EXLCZ)9928162819000041 100 $a20230907d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLectures on the Random Field Ising Model $eFrom Parisi-Sourlas Supersymmetry to Dimensional Reduction /$fby Slava Rychkov 205 $a1st ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (71 pages) 225 1 $aSpringerBriefs in Physics,$x2191-5431 311 $a9783031419997 327 $a1 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. 330 $aThis book is about the Random Field Ising Model (RFIM) ? a paradigmatic spin model featuring a frozen disordering field. The focus is on the second-order phase transition between the paramagnetic and ferromagnetic phases, and the associated critical exponents. The book starts by summarizing the current knowledge about the RFIM from experiments, numerical simulations and rigorous mathematical results. It then reviews the classic theoretical works from the 1970?s which suggested a property of dimensional reduction ? that the RFIM critical exponents should be the same as for the ordinary, non-disordered, Ising model of lower dimensionality, and related this an emergent Parisi-Sourlas supersymmetry. As is now known, these remarkable properties only hold when the spatial dimensionality of the model is larger than a critical dimension. The book presents a method to estimate the critical dimension, using standard tools such as the replica trick and perturbative renormalization group, whose result is in agreement with the numerical simulations. Some more elementary steps in the derivations are left as exercises for the readers. This book is of interest to researchers, PhD students and advanced master students specializing in statistical field theory. 410 0$aSpringerBriefs in Physics,$x2191-5431 606 $aStatistical Physics 606 $aParticles (Nuclear physics) 606 $aMathematical physics 606 $aStatistical Physics 606 $aParticle Physics 606 $aTheoretical, Mathematical and Computational Physics 615 0$aStatistical Physics. 615 0$aParticles (Nuclear physics). 615 0$aMathematical physics. 615 14$aStatistical Physics. 615 24$aParticle Physics. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a530.13 700 $aRychkov$b Slava$0821812 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910746090403321 996 $aLectures on the Random Field Ising Model$93563132 997 $aUNINA