Self-avoiding walk, spin systems and renormalization

2018/08/31 by Gordon Slade · 16 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Critical phenomena #Lattice (music) #Mathematical model #Quantum Computing Algorithms and Architecture #Renormalization #Renormalization group #Spin (aerodynamics) #Theoretical and Computational Physics #math-ph #math.MP #math.PR #msc:60K35 #msc:82B20 #msc:82B27 #msc:82B28 #msc:82B41

paper · pdf · doi:10.1098/rspa.2018.0549

published in Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences 475(2221), 20180549 (Royal Society) · Minor edits. To appear in Proc. R. Soc. London, Series A

openalex created_date 2018/08/22 · arxiv created 2018/12/28 · openalex publication_date 2019/01/01 · arxiv updated 2019/03/06 · openalex updated_date 2026/08/05

Abstract

model, are models of interest both in mathematics and in physics. Many of their important mathematical problems remain unsolved, particularly those involving critical exponents. We survey some of these problems, and report on recent advances in their mathematical understanding via a rigorous non-perturbative renormalization group method.

Citations

• The renormalization group and the ε expansion
• Some theorems on stable processes
• Critical Exponents in 3.99 Dimensions
• Logarithmic Corrections to the Molecular-Field Behavior of Critical and Tricritical Systems
• Infrared bounds, phase transitions and continuous symmetry breaking
• Solving the 3d Ising Model with the Conformal Bootstrap II. c c -Minimization and Precise Critical Exponents
• Self-Avoiding Walk is Sub-Ballistic