WORLD SCIENTIFIC eBooks· 2018· Book chapter
The two-dimensional Ising model
- 1,255citations
- 2018year
Short summary
The 2D Ising model in a magnetic field reveals an unexpected natural boundary phenomenon in magnetic susceptibility, suggesting the scaling theory may be incomplete for H=0.
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Key points
- The 2D Ising model in a magnetic field is a simple system to study the relationship between integrable and non-integrable models.
- Magnetic susceptibility in this model has revealed an unexpected natural boundary phenomenon.
- This phenomenon, linked with Fermionic representations, suggests potential incompleteness in scaling theory for H=0.
AI-generated from the title and abstract; the full text is not read.
Abstract
Understanding the relationship which integrable (solvable) models, all of which possess very special symmetry properties, have with the generic nonintegrable 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.
The authors' abstract, as published at the source. WORLD SCIENTIFIC eBooks, 2018 · DOI ↗
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Field: Statistical and Nonlinear Physics
Statistical and Nonlinear PhysicsPhysics and Astronomy