We consider the Ginzburg-Landau Hamiltonian with a cubic-symmetric quartic interaction and compute the renormalization-group functions to six-loop order in d=3. We analyze the stability of the fixed points using a Borel transformation and a conformal mapping that takes into account the singularities of the Borel transform. We find that the cubic fixed point is stable for N>N(c), N(c)=2.89(4). Therefore, the critical properties of cubic ferromagnets are not described by the Heisenberg isotropic Hamiltonian, but instead by the cubic model at the cubic fixed point. For N=3, the critical exponents at the cubic and symmetric fixed points differ very little (less than the precision of our results, which is less than or similar to 1% in the case of gamma and nu). Moreover? the irrelevant interaction bringing from the symmetric to the cubic fixed point gives rise to slowly decaying scaling corrections with exponent omega(2)=0.010(4). For N=2, the isotropic fixed point is stable and the cubic interaction induces scaling corrections with exponent omega(2)=0.103(8). These conclusions are confirmed by a similar analysis of the five-loop epsilon expansion. A constrained analysis, which takes into account that N(c)=2 in two dimensions, gives N(c)=2.87(5).

N-component Ginzburg-Laudau Hamiltonian with cubic anisotropy: A six-loop study

VICARI, ETTORE
2000-01-01

Abstract

We consider the Ginzburg-Landau Hamiltonian with a cubic-symmetric quartic interaction and compute the renormalization-group functions to six-loop order in d=3. We analyze the stability of the fixed points using a Borel transformation and a conformal mapping that takes into account the singularities of the Borel transform. We find that the cubic fixed point is stable for N>N(c), N(c)=2.89(4). Therefore, the critical properties of cubic ferromagnets are not described by the Heisenberg isotropic Hamiltonian, but instead by the cubic model at the cubic fixed point. For N=3, the critical exponents at the cubic and symmetric fixed points differ very little (less than the precision of our results, which is less than or similar to 1% in the case of gamma and nu). Moreover? the irrelevant interaction bringing from the symmetric to the cubic fixed point gives rise to slowly decaying scaling corrections with exponent omega(2)=0.010(4). For N=2, the isotropic fixed point is stable and the cubic interaction induces scaling corrections with exponent omega(2)=0.103(8). These conclusions are confirmed by a similar analysis of the five-loop epsilon expansion. A constrained analysis, which takes into account that N(c)=2 in two dimensions, gives N(c)=2.87(5).
2000
Carmona, Jm; Pelissetto, A; Vicari, Ettore
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/160825
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