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Confluent singularities in 3D continuum Φ4 theory: resolving critical point discrepancies

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  • Nickel, Bernie G.

Abstract

A new analysis of the three-dimensional ∅4 continuum model series for critical exponents and amplitude ratios is presented. By explicitly allowing for a second correction to scaling term with exponent ω2 and ω2/ω1 ≈ 2.0, a revision is found of previous critical point estimates that are all in the direction of resolving the remaining discrepancies between the 3D and 4 - ϵ analyses. The new estimates are also consistent with those obtained from high temperature series analyses of 3D lattice Ising models. For example, the exponents γ = 1.238, ν = 0.630, η = 0.0355 and correction to scaling amplitude ratio ɐξ/ɐχ = 0.77 are easily accommodated and possibly even preferred. Detailed verification will require further terms both in the low order perturbation theory and the high order asymptotic expansions.

Suggested Citation

  • Nickel, Bernie G., 1991. "Confluent singularities in 3D continuum Φ4 theory: resolving critical point discrepancies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 177(1), pages 189-196.
    • Handle: RePEc:eee:phsmap:v:177:y:1991:i:1:p:189-196
    DOI: 10.1016/0378-4371(91)90152-3
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