Zero-temperature renormalization-group method for quantum systems. III. Ising model in a transverse field in two dimensions

1979 ◽  
Vol 19 (9) ◽  
pp. 4653-4660 ◽  
Author(s):  
K. A. Penson ◽  
R. Jullien ◽  
P. Pfeuty
Keyword(s):  
Renormalization Group ◽  
Ising Model ◽  
Transverse Field ◽  
Quantum Systems ◽  
Two Dimensions ◽  
Group Method ◽  
Zero Temperature ◽  
Renormalization Group Method

A RIGOROUS RENORMALIZATION GROUP METHOD FOR INTERFACES IN RANDOM MEDIA

1994 ◽  
Vol 06 (03) ◽  
pp. 413-496 ◽  
Author(s):  
ANTON BOVIER ◽  
CHRISTOF KÜLSKE
Keyword(s):  
Renormalization Group ◽  
Ising Model ◽  
Low Temperature ◽  
Low Temperatures ◽  
Hierarchical Models ◽  
Random Media ◽  
Group Method ◽  
Renormalization Group Method ◽  
Weak Disorder ◽  
Random Field Ising Model

We prove the existence Gibbs states describing rigid interfaces in a disordered solid-on-solid (SOS) for low temperatures and for weak disorder in dimension D ≥ 4. This extends earlier results for hierarchical models to the more realistic models and proves a long-standing conjecture. The proof is based on the renormalization group method of Bricmont and Kupiainen originally developed for the analysis of low-temperature phases of the random field Ising model. In a broader context, we generalize this method to a class of systems with non-compact single-site state space.

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