TY - JOUR
T1 - Localization for a Nonlinear Sigma Model in a Strip Related to Vertex Reinforced Jump Processes
AU - Disertori, Margherita
AU - Merkl, Franz
AU - Rolles, Silke W.W.
N1 - Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.
PY - 2014/12/1
Y1 - 2014/12/1
N2 - We study a lattice sigma model which is expected to reflect Anderson localization and delocalization transition for real symmetric band matrices in 3D, but describes the mixing measure for a vertex reinforced jump process too. For this model we prove exponential localization at any temperature in a strip, and more generally in any quasi-one dimensional graph, with pinning (mass) at only one site. The proof uses a Mermin–Wagner type argument and a transfer operator approach.
AB - We study a lattice sigma model which is expected to reflect Anderson localization and delocalization transition for real symmetric band matrices in 3D, but describes the mixing measure for a vertex reinforced jump process too. For this model we prove exponential localization at any temperature in a strip, and more generally in any quasi-one dimensional graph, with pinning (mass) at only one site. The proof uses a Mermin–Wagner type argument and a transfer operator approach.
UR - http://www.scopus.com/inward/record.url?scp=84908128380&partnerID=8YFLogxK
U2 - 10.1007/s00220-014-2102-1
DO - 10.1007/s00220-014-2102-1
M3 - Article
AN - SCOPUS:84908128380
SN - 0010-3616
VL - 332
SP - 783
EP - 825
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -