The importance of the Ising model

Abstract

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 $H\ne 0$.

33 pages

References in corpus (5)

• Experimental mathematics on the magnetic susceptibility of the square lattice Ising model
• The diagonal Ising susceptibility
• On Properties of the Ising Model for Complex Energy/Temperature and Magnetic Field
• Inelastic scattering and elastic amplitude in Ising field theory in a weak magnetic field at T>T_c. Perturbative analysis
• Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model

Cited by in corpus (2)

• Phase transition in the majority-vote model on the Archimedean lattices
• From Network Reliability to the Ising Model: A Parallel Scheme for Estimating the Joint Density of States