The Ising Susceptibility Scaling Function

Abstract

We have dramatically extended the zero field susceptibility series at both high and low temperature of the Ising model on the triangular and honeycomb lattices, and used these data and newly available further terms for the square lattice to calculate a number of terms in the scaling function expansion around both the ferromagnetic and, for the square and honeycomb lattices, the antiferromagnetic critical point.

PDFLaTeX, 50 pages, 5 figures, zip file with series coefficients and background data in Maple format provided with the source files. Vs2: Added dedication and made several minor additions and corrections. Vs3: Minor corrections. Vs4: No change to eprint. Added essential square-lattice series input data (used in the calculation) that were removed from University of Melbourne's website

References in corpus (3)

• Experimental mathematics on the magnetic susceptibility of the square lattice Ising model
• Scaling and universality in the 2D Ising model with a magnetic field
• Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model

Cited by in corpus (27)

• Finite-size scaling at quantum transitions
• The importance of the Ising model
• Normal form for renormalization groups
• Exploring different regimes in finite-size scaling of the droplet condensation-evaporation transition
• Series extension: Predicting approximate series coefficients from a finite number of exact coefficients
• The $Z$-invariant Ising model via dimers
• Analyticity of Quantum States in One-Dimensional Tight-Binding Model
• Analysis of series expansions for non-algebraic singularities
• Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals
• Exact solutions to plaquette Ising models with free and periodic boundaries
• Spontaneous magnetization of Kagome lattice in Ising model
• The anisotropic Ising correlations as elliptic integrals: duality and differential equations
• Grassmannization of classical models
• Integrability vs non-integrability: Hard hexagons and hard squares compared
• Corner Transfer Matrix Approach to the Yang-Lee Singularity in the 2D Ising Model in a magnetic field
• Is the full susceptibility of the square-lattice Ising model a differentially algebraic function?
• Scaling functions in the square Ising model
• On the diagonal susceptibility of the 2D Ising model
• Universality in the 2d quasi-periodic Ising model and Harris-Luck irrelevance
• An exact local mapping from clock-spins to fermions
• Asymptotic correlation functions in the $Q$-state Potts model: a universal form for point group $C_{4v}$
• Large-order aspects of the delta-expansion in low-dimensional Ising models
• The diagonal two-point correlations of the Ising model on the anisotropic triangular lattice and Garnier systems
• Quasicrystals -- The impact of N.G. de Bruijn
• Universal asymptotic correlation functions for point group ${\mathbf{C}}_{6\mathbf{v}}$ and an observation for triangular lattice $\mathbf{Q}$-state Potts model
• Magnetic susceptibility of the square lattice Ising model
• On the Singularities in the Susceptibility Expansion for the Two-Dimensional Ising Model