scholarly journals Complete graph and Gaussian fixed-point asymptotics in the five-dimensional Fortuin-Kasteleyn Ising model with periodic boundaries

2020 ◽  
Vol 102 (2) ◽  
Author(s):  
Sheng Fang ◽  
Jens Grimm ◽  
Zongzheng Zhou ◽  
Youjin Deng
Keyword(s):  
Fixed Point ◽  
Ising Model ◽  
Complete Graph ◽  
Periodic Boundaries

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 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.

scholarly journals Percolation effects in the Fortuin-Kasteleyn Ising model on the complete graph

2021 ◽  
Vol 103 (1) ◽  
Author(s):  
Sheng Fang ◽  
Zongzheng Zhou ◽  
Youjin Deng
Keyword(s):  
Ising Model ◽  
Complete Graph

scholarly journals Non-perturbative effects in spin glasses

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Michele Castellana ◽  
Giorgio Parisi
Keyword(s):  
Fixed Point ◽  
Ising Model ◽  
Spin Glasses ◽  
Numerical Study ◽  
Mean Field ◽  
Critical Dimension ◽  
Upper Critical Dimension ◽  
Ising Spin ◽  
Ferromagnetic Ising Model ◽  
The Mean

Abstract We present a numerical study of an Ising spin glass with hierarchical interactions—the hierarchical Edwards-Anderson model with an external magnetic field (HEA). We study the model with Monte Carlo (MC) simulations in the mean-field (MF) and non-mean-field (NMF) regions corresponding to d ≥ 4 and d < 4 for the d-dimensional ferromagnetic Ising model respectively. We compare the MC results with those of a renormalization-group (RG) study where the critical fixed point is treated as a perturbation of the MF one, along the same lines as in the "Equation missing"-expansion for the Ising model. The MC and the RG method agree in the MF region, predicting the existence of a transition and compatible values of the critical exponents. Conversely, the two approaches markedly disagree in the NMF case, where the MC data indicates a transition, while the RG analysis predicts that no perturbative critical fixed point exists. Also, the MC estimate of the critical exponent ν in the NMF region is about twice as large as its classical value, even if the analog of the system dimension is within only ~2% from its upper-critical-dimension value. Taken together, these results indicate that the transition in the NMF region is governed by strong non-perturbative effects.

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 Strong-Disorder Paramagnetic-Ferromagnetic Fixed Point in the Square-Lattice ±J Ising Model

2009 ◽  
Vol 135 (5-6) ◽  
pp. 1039-1061 ◽  
Author(s):  
Francesco Parisen Toldin ◽  
Andrea Pelissetto ◽  
Ettore Vicari
Keyword(s):  
Fixed Point ◽  
Ising Model ◽  
Square Lattice ◽  
Strong Disorder
Sign in / Sign up

Export Citation Format

Share Document