München 1997 – scientific programme

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 5: Quantenfeldtheorie

MP 5.3: Fachvortrag

Wednesday, March 19, 1997, 16:40–17:00, HS 110

Stability of 3D Cubic Fixed Point in Two-Coupling-Constant φ⁴-Theory — •Silke Thoms and Verena Schulte-Frohlinde — Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin

For an anisotropic euclidean φ⁴-theory with two interactions
[u (∑_i=1^M φ_i²)²+v ∑_i=1^M φ_i⁴] the renormalization group functions are calculated perturbatively up to five loops in d=4−ε dimensions [1]. Furthermore, the large-order behavior of the renormalization group functions is calculated in form of a series expansion in v, i. e. around the isotropic case [2]. Combining both informations, the β-functions are determined by using a Borel-type of resummation algorithm [3].

For ε=1, an infrared stable cubic fixed point for M ≥ 3 is found, implying that the critical exponents in the magnetic phase transition of real crystals are of the cubic universality class. There were previous indications of the stability based either on lower-loop expansions or on less reliable Padé approximations, but only the evidence presented here seems to be sufficently convincing to draw this conclusion.

[1] H. Kleinert, V. Schulte-Frohlinde, Phys. Lett. B 342, 284 (1995)

[2] H. Kleinert, S. Thoms, Phys. Rev. D 52(10), 5926 (1995)

[3] H. Kleinert, S. Thoms and V. Schulte-Frohlinde, to be published