We use the method of infinitesimal unitary transformations to calculate zero-temperature correlation functions in the strong-coupling phase of the anisotropic Kondo model. We find the dynamics on all energy scales including the crossover behavior from weak to strong coupling. The integrable structure of the Hamiltonian is not used in our approach. Our method should also be useful in other strong-coupling models since few other analytical methods allow the evaluation of their correlation functions on all energy scales.We use the method of infinitesimal unitary transformations to calculate zero-temperature correlation functions in the strong-coupling phase of the anisotropic Kondo model. We find the dynamics on all energy scales including the crossover behavior from weak to strong coupling. The integrable structure of the Hamiltonian is not used in our approach. Our method should also be useful in other strong-coupling models since few other analytical methods allow the evaluation of their correlation functions on all energy scales.

arXiv:cond-mat/0008242Physical review. B, Condensed matterMar 2, 200124 citations

Anisotropic vertex models

R. Z. Bariev, Yu.V. Kozhinov

Physics Letters AOct 1, 19823 citations

On the symmetry of universal finite-size scaling functions in anisotropic systems

Alfred Hucht

We postulate a symmetry of universal finite-size scaling functions under a certain anisotropic scale transformation, which connects the properties of a finite two-dimensional (2D) system at criticality with generalized aspect ratio ρ > 1 to a system with ρ < 1. The symmetry is formulated within a finite-size scaling theory and expressions for several universal amplitude ratios are derived. The predictions are confirmed within the exactly solvable weakly anisotropic 2D Ising model and are checked within the strongly anisotropic 2D dipolar in-plane Ising model using Monte Carlo simulations.We postulate a symmetry of universal finite-size scaling functions under a certain anisotropic scale transformation, which connects the properties of a finite two-dimensional (2D) system at criticality with generalized aspect ratio ρ > 1 to a system with ρ < 1. The symmetry is formulated within a finite-size scaling theory and expressions for several universal amplitude ratios are derived. The predictions are confirmed within the exactly solvable weakly anisotropic 2D Ising model and are checked within the strongly anisotropic 2D dipolar in-plane Ising model using Monte Carlo simulations.

arXiv:cond-mat/0202142Journal of Physics A Mathematical and GeneralJul 25, 200229 citations

Finite-Size Scaling

A. P. Young

WORLD SCIENTIFIC eBooksAug 1, 20240 citations

Local Scale Invariance and Strongly Anisotropic Equilibrium Critical Systems

Malte Henkel

A new set of infinitesimal transformations generalizing scale invariance for strongly anisotropic critical systems is considered. It is shown that such a generalization is possible if the anisotropy exponent $\ensuremath{\theta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2/N$, with $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1,2,3\dots{}$ . Differential equations for the two-point function are derived and explicitly solved for all values of $N$ . Known special cases are conformal invariance ( $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ ) and Schr\"odinger invariance ( $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ ). For $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4$ and $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}6$ , the results contain as special cases the exactly known scaling forms obtained for the spin-spin correlation function in the axial next-nearest-neighbor spherical model at its Lifshitz points of first and second order.A new set of infinitesimal transformations generalizing scale invariance for strongly anisotropic critical systems is considered. It is shown that such a generalization is possible if the anisotropy exponent $\ensuremath{\theta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2/N$, with $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1,2,3\dots{}$. Differential equations for the two-point function are derived and explicitly solved for all values of $N$. Known special cases are conformal invariance ( $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$) and Schr\"odinger invariance ( $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$). For $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4$ and $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}6$, the results contain as special cases the exactly known scaling forms obtained for the spin-spin correlation function in the axial next-nearest-neighbor spherical model at its Lifshitz points of first and second order.

arXiv:cond-mat/9610174Physical Review LettersMar 10, 1997118 citations

N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1,2,3\dots{}

. Differential equations for the two-point function are derived and explicitly solved for all values of

N

. Known special cases are conformal invariance (

N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2

) and Schr\"odinger invariance (

N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

). For

N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4

and

N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}6

, the results contain as special cases the exactly known scaling forms obtained for the spin-spin correlation function in the axial next-nearest-neighbor spherical model at its Lifshitz points of first and second order.