Critical equation of state of randomly dilute Ising systems

Abstract

We determine the critical equation of state of three-dimensional randomly dilute Ising systems, i.e. of the random-exchange Ising universality class. We first consider the small-magnetization expansion of the Helmholtz free energy in the high-temperature phase. Then, we apply a systematic approximation scheme of the equation of state in the whole critical regime, that is based on polynomial parametric representations matching the small-magnetization of the Helmholtz free energy and satisfying a global stationarity condition. These results allow us to estimate several universal amplitude ratios, such as the ratio A^+/A^- of the specific-heat amplitudes. Our best estimate A^+/A^-=1.6(3) is in good agreement with experimental results on dilute uniaxial antiferromagnets.

arXiv comment21 pages, 1 figure, refs added

References in corpus (22)

• Critical Phenomena and Renormalization-Group Theory
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Critical behavior of the three-dimensional XY universality class
• 25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice
• Critical exponents of the three dimensional diluted Ising model
• 3D Ising Model:The Scaling Equation of State
• Addendum-erratum to: ``Nonasymptotic critical behavior from field theory at d=3. II. The ordered-phase case. Phys. Rev. B35, 3585 (1987)
• Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems
• Randomly dilute spin models: a six-loop field-theoretic study
• Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus ${\epsilon }^{1/2}$-Expansion
• Five-loop renormalization-group expansions for the three-dimensional n-vector cubic model and critical exponents for impure Ising systems
• The three-dimensional randomly dilute Ising model: Monte Carlo results
• Five-loop \sqrtε-expansions for random Ising model and marginal spin dimensionality for cubic systems
• Randomly dilute Ising model: A nonperturbative approach
• Summability of the perturbative expansion for a zero-dimensional disordered spin model
• The effective potential of N-vector models: a field-theoretic study to O(ε^3)
• The critical equation of state of the 2D Ising model
• The critical equation of state of three-dimensional XY systems
• The correction-to-scaling exponent in dilute systems
• Renormalization group and nonlinear susceptibilities of cubic ferromagnets at criticality
• Crossover from random-exchange to random-field critical behavior in Ising models
• Nonlinear susceptibilities of a weakly-disordered uniaxial ferromagnet in the critical region

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• Field-theory results for three-dimensional transitions with complex symmetries
• Static and dynamic structure factors in three-dimensional randomly diluted Ising models
• Critical fluctuations in the spin-orbit Mott insulator Sr${}_3$Ir${}_2$O${}_7$