Critical thermodynamics of the two-dimensional systems in five-loop renormalization-group approximation

Details Critical thermodynamics of the two-dimensional systems in five-loop renormalization-group approximation Critical thermodynamics of the two-dimensional systems in five-loop renormalization-group approximation

2000-03-16

arxiv.org/abs/hep-th/0003140v4

Fizika Tverdogo Tela 42, No 11, 2087-2093 (2000)

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 6 pages, concise English version of the paper published, in Russian, in Fizika Tverdogo Tela (Physics of the Solid Stat

Scientific paper

The RG functions of the 2D n-vector \phi^4 model are calculated in the five-loop approximation. Perturbative series for the \beta-function and critical exponents are resummed by the Pade-Borel and Pade-Borel-Leroy techniques, resummation procedures are optimized and an accuracy of the numerical results is estimated. In the Ising case n = 1 as well as in the others (n = 0, n = -1, n = 2, 3,...32) an account for the five-loop term is found to shift the Wilson fixed point location only briefly, leaving it outside the segment formed by the results of the corresponding lattice calculations; even error bars of the RG and lattice estimates do not overlap in the most cases studied. This is argued to reflect the influence of the singular (non-analytical) contribution to the \beta-function that can not be found perturbatively. The evaluation of the critical exponents for n = 1, n = 0 and n = -1 in the five-loop approximation and comparison of the numbers obtained with their known exact counterparts confirm the conclusion that non-analytical contributions are visible in two dimensions. For the 2D Ising model, the estimates \omega = 1.31(3) for the correction-to-scaling exponent is found that is close to the value 4/3 resulting from the conformal invariance.

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