scholarly journals Renormalization group flows in one-dimensional lattice models: Impurity scaling, umklapp scattering, and the orthogonality catastrophe

2014 ◽  
Vol 90 (15) ◽  
Author(s):  
D. M. Kennes ◽  
M. J. Schmidt ◽  
D. Hübscher ◽  
V. Meden
Keyword(s):  
Renormalization Group ◽  
Lattice Models ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Renormalization Group Flows ◽  
Umklapp Scattering

Finite-size scaling studies of massive one-dimensional lattice models

2001 ◽  
Vol 64 (10) ◽  
Author(s):  
Liu Yichang ◽  
Jianhui Dai ◽  
Shaojin Qin ◽  
Lu Yu
Keyword(s):  
Finite Size ◽  
Lattice Models ◽  
Finite Size Scaling ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Size Scaling

HIERARCHICAL TRAPPING ON A ONE-DIMENSIONAL LATTICE

1994 ◽  
Vol 08 (06) ◽  
pp. 399-405 ◽  
Author(s):  
ACHILLE GIACOMETTI
Keyword(s):  
Renormalization Group ◽  
Numerical Simulations ◽  
Critical Exponents ◽  
Qualitative Agreement ◽  
Total Probability ◽  
Transition Rates ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Ideal Chain ◽  
Universal Values

The effect of the nonconservation of the total probability in the presence of a hierarchy of transition rates is studied by renormalization group techniques and confirmed by numerical simulations on a one-dimensional lattice. The model can be considered as the static (or ideal chain) counterpart of the Hubermann-Kerszberg model. It is found that critical exponents are always nonuniversal in the presence of a hierarchy and jump discontinuously to universal values in the limit of no hierarchy. Qualitative agreement with recent simulations is found.

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