Finite Size Scaling of Classical Long-Ranged Ising Chains and the Criticality of Dissipative Quantum Impurity Models
arXiv:0808.0916 · doi:10.1103/PhysRevLett.102.166405
Abstract
Motivated in part by quantum criticality in dissipative Kondo systems, we revisit the finite-size scaling of a classical Ising chain with 1/r^{2-epsilon} interactions. For 1/2<epsilon<1, the scaling of the dynamical spin susceptibility is sensitive to the degree of "winding" of the interaction under periodic boundary conditions. Infinite winding yields the expected mean-field behavior, whereas without any winding the scaling is of an interacting omega/T form. The contrast with the behavior of the Bose-Fermi Kondo model suggests a breakdown of a mapping from the quantum model to a classical one due to the smearing of the Kondo spin flips by the continuum limit taken in this mapping.
arXiv comment4 pages, 3 figures; published version
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