Crossover scaling: A renormalization group approach

@article{OConnor1994CrossoverSA,
  title={Crossover scaling: A renormalization group approach},
  author={Denjoe O’Connor and Christopher R. Stephens},
  journal={Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences},
  year={1994},
  volume={444},
  pages={287 - 296}
}
  • D. O’ConnorC. Stephens
  • Published 8 February 1994
  • Physics
  • Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
We derive a theory of crossover scaling based on a scaling variable gξg, where g is the anisotropy parameter inducing the crossover and ξg is the correlation length in the presence of g. Our considerations are field theoretic and based on a renormalization group with a g dependent differential generator that interpolates between qualitatively different degrees of freedom. ξg is a nonlinear scaling field for this renormalization group and interpolates between (T – Tc(g))–v0 and (T – Tc(g))–v… 
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References

SHOWING 1-10 OF 17 REFERENCES

Dimensional crossover and finite-size scaling belowTc

Using the formalism developed in earlier work, dimensional crossover on ad-dimensional layered Ising-type system satisfying periodic boundary conditions and of sizeL is considered belowTc(L), Tc(L)

Finite-size scaling and the renormalization group

Renormalization group calculations ind = 4 andd = 4 −ɛ are performed for a system of finite size. A form of mean-field theory is used which yields a rounded transition for a finite system, and this

Scaling approach to anisotropic magnetic systems statics

Scaling laws are stated for anisotropic magnetic systems, where the anisotropy parameters are either scaled or held fixed. Combining the two ways of scaling, the critical behavior of thermodynamic

Critical phenomena during a dimensional crossover

The critical behaviour of a system undergoing a dimensional crossover is investigated. A renormalization group equation is obtained that interpolates between different dimensions. The susceptibility

Renormalized field theory for the static crossover in uniaxial dipolar ferromagnets.

  • FreySchwabl
  • Physics
    Physical review. B, Condensed matter
  • 1990
Within a generalized minimal subtraction scheme, the crossover from Ising behavior with nonclassical exponents to asymptotic uniaxial dipolar behavior, which is characterized by classical exponents with logarithmic corrections is described.

Critical Indices from Perturbation Analysis of the Callan-Symanzik Equation

Recent results giving both the asymptotic behavior and the explicit values of the leading-order perturbation-expansion terms in fixed dimension for the coefficients of the Callan-Symanzik equation

Finite-size scaling of the superfluid density of 4He confined between silicon wafers.

These are the first measurements of helium confined in a sufficiently well-defined planar geometry to show a crossover from three-dimensional-like to finite-size to two-dimensional behavior.