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

Massimo Campostrini·Andrea Pelissetto·Paolo Rossi·Ettore Vicari
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Abstract

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: $γ=1.2371(4)$, $ν=0.63002(23)$, $α=0.1099(7)$, $η=0.0364(4)$, $β=0.32648(18)$. 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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Massimo Campostrini, Andrea Pelissetto, Paolo Rossi, Ettore Vicari. 1999-06-21. Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems. https://doi.org/10.1103/physreve.60.3526

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