Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems

Details Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems

1999-05-06

arxiv.org/abs/cond-mat/9905078v2

Phys.Rev. E60 (1999) 3526-3563

Physics

Condensed Matter

Statistical Mechanics

65 pages, 1 figure, revtex. New Monte Carlo data by Hasenbusch enabled us to improve the determination of the critical exponen

Scientific paper

10.1103/PhysRevE.60.3526

High-temperature series are computed for a generalized $3d$ Ising model with arbitrary potential. Two specific ``improved'' potentials (suppressing leading scaling corrections) are selected by Monte Carlo computation. Critical exponents are extracted from high-temperature series specialized to improved potentials, achieving high accuracy; our best estimates are: $\gamma=1.2371(4)$, $\nu=0.63002(23)$, $\alpha=0.1099(7)$, $\eta=0.0364(4)$, $\beta=0.32648(18)$. By the same technique, the coefficients of the small-field expansion for the effective potential (Helmholtz free energy) are computed. These results are applied to the construction of parametric representations of the critical equation of state. A systematic approximation scheme, based on a global stationarity condition, is introduced (the lowest-order approximation reproduces the linear parametric model). This scheme is used for an accurate determination of universal ratios of amplitudes. A comparison with other theoretical and experimental determinations of universal quantities is presented.

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