Exact renormalization group exhibiting tricritical fixed point for a spin-one Ising model in one dimension

1975 ◽  
Vol 11 (7) ◽  
pp. 2602-2611 ◽  
Author(s):  
S. Krinsky ◽  
D. Furman
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Ising Model ◽  
One Dimension ◽  
Exact Renormalization Group

scholarly journals FIELD BEHAVIOR OF AN ISING MODEL WITH APERIODIC INTERACTIONS

2000 ◽  
Vol 14 (14) ◽  
pp. 1473-1480
Author(s):  
ANGSULA GHOSH ◽  
T. A. S. HADDAD ◽  
S. R. SALINAS
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Ising Model ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Exchange Interactions ◽  
Universality Class ◽  
Recursion Relations ◽  
Hierarchical Lattices ◽  
Exact Renormalization Group

We derive exact renormalization-group recursion relations for an Ising model, in the presence of external fields, with ferromagnetic nearest-neighbor interactions on Migdal–Kadanoff hierarchical lattices. We consider layered distributions of aperiodic exchange interactions, according to a class of two-letter substitutional sequences. For irrelevant geometric fluctuations, the recursion relations in parameter space display a nontrivial uniform fixed point of hyperbolic character that governs the universal critical behavior. For relevant fluctuations, in agreement with previous work, this fixed point becomes fully unstable, and there appears a two-cycle attractor associated with a new critical universality class.

scholarly journals The cubic fixed point at large N

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Damon J. Binder
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Ising Model ◽  
Ising Models ◽  
Three Dimensions ◽  
Renormalization Group Flow ◽  
Conformal Bootstrap ◽  
Large N ◽  
Group Flow ◽  
3D Ising Model

Abstract By considering the renormalization group flow between N coupled Ising models in the UV and the cubic fixed point in the IR, we study the large N behavior of the cubic fixed points in three dimensions. We derive a diagrammatic expansion for the 1/N corrections to correlation functions. Leading large N corrections to conformal dimensions at the cubic fixed point are then evaluated using numeric conformal bootstrap data for the 3d Ising model.

scholarly journals Products of current operators in the exact renormalization group formalism

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
H. Sonoda
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Short Distance ◽  
Multiple Products ◽  
Exact Renormalization Group

Abstract Given a Wilson action invariant under global chiral transformations, we can construct current composite operators in terms of the Wilson action. The short-distance singularities in the multiple products of the current operators are taken care of by the exact renormalization group. The Ward–Takahashi identity is compatible with the finite momentum cutoff of the Wilson action. The exact renormalization group and the Ward–Takahashi identity together determine the products. As a concrete example, we study the Gaussian fixed-point Wilson action of the chiral fermions to construct the products of current operators.

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.

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