2012/03/07 by Barry M. McCoy, B. M. McCoy, J-M Maillard +1 · 36 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Boundary (topology) #Boundary value problem #Conformal field theory #Conformal map #Geometry #Integrable system #Ising model #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum many-body systems #Quantum mechanics #Scaling #Square-lattice Ising model #Statistical mechanics #Statistical physics #Symmetry (geometry) #Symmetry breaking #Theoretical and Computational Physics #Theoretical physics #cond-mat.stat-mech #hep-th #math-ph #math.MP #msc:14Kxx #msc:32G34 #msc:34Lxx #msc:34M55 #msc:34Mxx #msc:47E05 #msc:81Qxx
paper · pdf · doi:10.1143/ptp.127.791
published in Progress of Theoretical Physics 127(5), 791-817 (Oxford University Press) · 33 pages
arxiv created 2012/03/07 · openalex publication_date 2012/05/01 · arxiv updated 2012/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Understanding the relationship which integrable (solvable) models, all of which possess very special symmetry properties, have with the generic non-integrable models that are used to describe real experiments, which do not have the symmetry properties, is one of the most fundamental open questions in both statistical mechanics and quantum field theory. The importance of the two-dimensional Ising model in a magnetic field is that it is the simplest system where this relationship may be concretely studied. We here review the advances made in this study, and concentrate on the magnetic susceptibility which has revealed an unexpected natural boundary phenomenon. When this is combined with the Fermionic representations of conformal characters, it is suggested that the scaling theory, which smoothly connects the lattice with the correlation length scale, may be incomplete for H ≠ 0.