Lectures on the Random Field Ising Model : From Parisi-Sourlas Supersymmetry to Dimensional Reduction

Preface
Contents
Acronyms
1 History, Basics, Experiments  and Simulations
	1.1 History
	1.2 Basic Facts
	1.3 Experiments
	1.4 Numerical Simulations
	References
2 Parisi–Sourlas Theory, Dimensional Reduction
	2.1 Field Theory and Perturbation Theory
	2.2 Connected and Disconnected 2pt Functions
	2.3 Selection of Important Diagrams
	2.4 Stochastic PDE Representation, Parisi–Sourlas Action
	2.5 Parisi–Sourlas Supersymmetry
	2.6 SUSY Ward Identities
	2.7 Dimensional Reduction
	2.8 Caveats
	2.9 Literature and Further Comments
	References
3 Replicas, Cardy Transform, Leaders, Loss of SUSY
	3.1 Replicas
	3.2 Upper Critical Dimension
	3.3 Cardy Transform: Second Argument for the PS SUSY
	3.4 Testing the Second Argument
	3.5 Analogies
	3.6 Leaders
	3.7 Classification of Leaders
	3.8 Renormalization Group Fixed Point and Its Stability
	3.9 Relation to Previous Work
	3.10 Literature and Further Comments
	References
4 Open Problems and Future Directions
	4.1 Symmetry Meaning of Leaders
	4.2 Branched Polymers
	4.3 Nonperturbative RG Studies of RFIM
	4.4 Tuning to the SUSY Fixed Point
	References