Critical behaviour of the two-dimensional Ising susceptibility

Abstract

We report computations of the short-distance and the long-distance (scaling) contributions to the square-lattice Ising susceptibility in zero field close to T_c. Both computations rely on the use of nonlinear partial difference equations for the correlation functions. By summing the correlation functions, we give an algorithm of complexity O(N^6) for the determination of the first N series coefficients. Consequently, we have generated and analysed series of length several hundred terms, generated in about 100 hours on an obsolete workstation. In terms of a temperature variable, τ, linear in T/T_c-1, the short-distance terms are shown to have the form τ^p(ln|τ|)^q with p>=q^2. To O(τ^14) the long-distance part divided by the leading τ^{-7/4} singularity contains only integer powers of τ. The presence of irrelevant variables in the scaling function is clearly evident, with contributions of distinct character at leading orders |τ|^{9/4} and |τ|^{17/4} being identified.

11 pages, REVTex 4

Cited by in corpus (29)

• New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain
• The Fuchsian differential equation of the square lattice Ising model $\chi (3)$ susceptibility
• Square lattice Ising model susceptibility: connection matrices and singular behavior of ${\chi }^{(3)}$ and ${\chi }^{(4)}$
• Square lattice Ising model susceptibility: Series expansion method and differential equation for ${\chi }^{(3)}$
• Exact Finite-Size-Scaling Corrections to the Critical Two-Dimensional Ising Model on a Torus. II. Triangular and hexagonal lattices
• Monte Carlo study of the evaporation/condensation transition on different Ising lattices
• Ising model susceptibility: Fuchsian differential equation for ${\chi }^{(4)}$ and its factorization properties
• The Ising Susceptibility Scaling Function
• The critical equation of state of the 2D Ising model
• Exploring different regimes in finite-size scaling of the droplet condensation-evaporation transition
• Correction induced by irrelevant operators in the correlators of the 2d Ising model in a magnetic field
• Analyticity of Quantum States in One-Dimensional Tight-Binding Model
• Susceptibility amplitude ratio in the two-dimensional three-state Potts model
• Study of the 2d Ising Model with mixed perturbation
• Critical parameters and universal amplitude ratios of two-dimensional spin-S Ising models using high- and low-temperature expansions
• Exact solutions to plaquette Ising models with free and periodic boundaries
• Extended Scaling for the high dimension and square lattice Ising Ferromagnets
• Extended scaling for ferromagnetic Ising models with zero-temperature transitions
• Critical scaling to infinite temperature
• Amplitude ratios for the mass spectrum of the 2d Ising model in the high-T, H \neq 0 phase
• Universal ratios of critical amplitudes in the Potts model universality class
• Exact solution and high temperature series expansion study of the 1/5-th depleted square lattice Ising model
• Some Recent Results on Pair Correlation Functions and Susceptibilities in Exactly Solvable Models
• Orientation Reversal and the Chern-Simons Natural Boundary
• Do hard spheres have natural boundaries?
• Beyond series expansions: mathematical structures for the susceptibility of the square lattice Ising model
• Approximate thermodynamics of the two-dimensional Ising model in an external magnetic field
• Magnetic susceptibility of quasi-one-dimensional Ising superantiferromagnets FeTAC and MCl_2*2NC_5H_5 (M=Co, Fe): Approximations with L x oo and L x L x oo chain clusters
• Magnetic susceptibility of the square lattice Ising model