Surface tension, roughening, and lower critical dimension in the random-field Ising model

1983 ◽  
Vol 28 (5) ◽  
pp. 2588-2601 ◽  
Author(s):  
G. Grinstein ◽  
Shang-keng Ma
Keyword(s):  
Surface Tension ◽  
Ising Model ◽  
Random Field ◽  
Critical Dimension ◽  
Random Field Ising Model

scholarly journals Random field Ising model and Parisi-Sourlas supersymmetry. Part II. Renormalization group

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Apratim Kaviraj ◽  
Slava Rychkov ◽  
Emilio Trevisani
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Ising Model ◽  
Random Field ◽  
Dimensional Reduction ◽  
Critical Dimension ◽  
Random Field Ising Model ◽  
Upper Critical Dimension ◽  
Anomalous Dimensions ◽  
Weakly Coupled

Abstract We revisit perturbative RG analysis in the replicated Landau-Ginzburg description of the Random Field Ising Model near the upper critical dimension 6. Working in a field basis with manifest vicinity to a weakly-coupled Parisi-Sourlas supersymmetric fixed point (Cardy, 1985), we look for interactions which may destabilize the SUSY RG flow and lead to the loss of dimensional reduction. This problem is reduced to studying the anomalous dimensions of “leaders” — lowest dimension parts of Sn-invariant perturbations in the Cardy basis. Leader operators are classified as non-susy-writable, susy-writable or susy-null depending on their symmetry. Susy-writable leaders are additionally classified as belonging to superprimary multiplets transforming in particular OSp(d|2) representations. We enumerate all leaders up to 6d dimension ∆ = 12, and compute their perturbative anomalous dimensions (up to two loops). We thus identify two perturbations (with susy- null and non-susy-writable leaders) becoming relevant below a critical dimension dc ≈ 4.2 - 4.7. This supports the scenario that the SUSY fixed point exists for all 3 < d ⩽ 6, but becomes unstable for d < dc.

Lower Critical Dimension of the Random-Field Ising Model: A Monte Carlo Study

1984 ◽  
Vol 52 (2) ◽  
pp. 145-148 ◽  
Author(s):  
David Andelman ◽  
H. Orland ◽  
L. C. R. Wijewardhana
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Random Field ◽  
Monte Carlo Study ◽  
Critical Dimension ◽  
Random Field Ising Model
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