Variational approach to the scaling function of the 2D Ising model in a magnetic field

Abstract

The universal scaling function of the square lattice Ising model in a magnetic field is obtained numerically via Baxter's variational corner transfer matrix approach. The high precision numerical data is in perfect agreement with the remarkable field theory results obtained by Fonseca and Zamolodchikov, as well as with many previously known exact and numerical results for the 2D Ising model. This includes excellent agreement with analytic results for the magnetic susceptibility obtained by Orrick, Nickel, Guttmann and Perk. In general the high precision of the numerical results underlines the potential and full power of the variational corner transfer matrix approach.

12 pages, 1 figure, 4 tables, v2: minor corrections, references added

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Cited by in corpus (14)

• Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms
• Scaling theory of the Mott transition and breakdown of the Grüneisen scaling near a finite-temperature critical end point
• 2D Ising Field Theory in a Magnetic Field: The Yang-Lee Singularity
• Scaling and universality in the 2D Ising model with a magnetic field
• Series expansions from the corner transfer matrix renormalization group method: the hard squares model
• The free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model
• Variational approach to the scaling function of the 2D Ising model in a magnetic field
• Radiative corrections to the quark masses in the ferromagnetic Ising and Potts field theories
• Corner Transfer Matrix Approach to the Yang-Lee Singularity in the 2D Ising Model in a magnetic field
• On the Yang-Lee and Langer singularities in the O(n) loop model
• Analyticity of the Ising susceptibility: An interpretation
• Accurate lower bounds on two-dimensional constraint capacities from corner transfer matrices
• Complete universal scaling of first-order phase transitions in the two-dimensional Ising model
• Smooth and global Ising universal scaling functions