The critical equation of state of the 2D Ising model

Abstract

We compute the 2n-point coupling constants in the high-temperature phase of the 2d Ising model by using transfer-matrix techniques. This provides the first few terms of the expansion of the effective potential (Helmholtz free energy) and of the equation of state in terms of the renormalized magnetization. By means of a suitable parametric representation, we determine an analytic extension of these expansions, providing the equation of state in the whole critical region in the t,h plane.

32 pages, 2 figures, new results added in sect.4

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Cited by in corpus (22)

• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• 25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice
• Irrelevant operators in the two-dimensional Ising model
• Ising field theory in a magnetic field: analytic properties of the free energy
• Characterization of resonances using finite size effects
• Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation
• Universal location of Yang-Lee edge singularity for a one-component field theory in $1\le d\le 4$
• Tethered Monte Carlo: computing the effective potential without critical slowing down
• Scaling and universality in the 2D Ising model with a magnetic field
• Critical behavior of the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy
• Variational approach to the scaling function of the 2D Ising model in a magnetic field
• Pseudo-$\epsilon$ Expansion and Renormalized Coupling Constants at Criticality
• 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
• Charting the scaling region of the Ising universality class in two and three dimensions
• Critical equation of state of randomly dilute Ising systems
• Effective potential of the three-dimensional Ising model: the pseudo-$\epsilon$ expansion study
• Amplitude ratios for the mass spectrum of the 2d Ising model in the high-T, H \neq 0 phase
• Finite temperature corrections in 2d integrable models
• Universal effective couplings of the three-dimensional $n$-vector model and field theory
• Finite temperature results on the 2d Ising model with mixed perturbation
• Equation of state for systems with Goldstone bosons