TY - JOUR
T1 - Chaos in the Mixed Even-Spin Models
AU - Chen, Wei Kuo
PY - 2014/6
Y1 - 2014/6
N2 - We consider a disordered system obtained by coupling two mixed even-spin models together. The chaos problem is concerned with the behavior of the coupled system when the external parameters in the two models, such as, temperature, disorder, or external field, are slightly different. It is conjectured that the overlap between two independently sampled spin configurations from, respectively, the Gibbs measures of the two models is essentially concentrated around a constant under the coupled Gibbs measure. Using the extended Guerra replica symmetry breaking bound together with a recent development of controlling the overlap using the Ghirlanda-Guerra identities as well as a new family of identities, we present rigorous results on chaos in temperature. In addition, chaos in disorder and in external field are addressed.
AB - We consider a disordered system obtained by coupling two mixed even-spin models together. The chaos problem is concerned with the behavior of the coupled system when the external parameters in the two models, such as, temperature, disorder, or external field, are slightly different. It is conjectured that the overlap between two independently sampled spin configurations from, respectively, the Gibbs measures of the two models is essentially concentrated around a constant under the coupled Gibbs measure. Using the extended Guerra replica symmetry breaking bound together with a recent development of controlling the overlap using the Ghirlanda-Guerra identities as well as a new family of identities, we present rigorous results on chaos in temperature. In addition, chaos in disorder and in external field are addressed.
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U2 - 10.1007/s00220-014-1888-1
DO - 10.1007/s00220-014-1888-1
M3 - Article
AN - SCOPUS:84900309759
SN - 0010-3616
VL - 328
SP - 867
EP - 901
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 3
ER -