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

May, 1999
62 pages
Published in:
  • Phys.Rev.E 60 (1999) 3526-3563
e-Print:
Report number:
  • IFUP-TH-22-99

Citations per year

19992005201120172021051015
Abstract: (APS)
High-temperature series are computed for a generalized three-dimensional Ising model with arbitrary potential. Three 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.