Randomly dilute Ising model: A nonperturbative approach

2001/09/30 by M. Tissier, Matthieu Tissier, D. Mouhanna +4 · 1 citation
Mathematics · Physics and Astronomy · #Anisotropy #Combinatorics #Complex Network Analysis Techniques #Condensed matter physics #Critical dimension #Critical exponent #Dimension (graph theory) #Ising model #Mathematical physics #Mathematics #Phase transition #Physics #Quantum many-body systems #Quantum mechanics #Renormalization group #Square-lattice Ising model #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevb.65.140402

published as Phys. Rev. B 65, 140402 (2002) · 4 pages, published version

openalex publication_date 2002/03/28 · arxiv created 2002/04/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The N-vector cubic model relevant, among others, to the physics of the randomly dilute Ising model is analyzed in arbitrary dimension by means of an exact renormalization-group equation. This study provides a unified picture of its critical physics between two and four dimensions. We give the critical exponents for the three-dimensional randomly dilute Ising model that are in good agreement with experimental and numerical data. The relevance of the cubic anisotropy in the O(N) model is also treated.

Citations

• The renormalization group and the ε expansion
• Effective and asymptotic critical exponents of a weakly diluted quenched Ising model: Three-dimensional approach versusɛexpansion
• The correction-to-scaling exponent in dilute systems
• Exact evolution equation for the effective potential
• Critical exponents from the effective average action
• Effect of random defects on the critical behaviour of Ising models
• Frustrated Heisenberg Magnets: A Nonperturbative Approach

Cited by

• The nonperturbative functional renormalization group and its applications