TY - JOUR
T1 - On the zero-temperature limit of gibbs states
AU - Chazottes, Jean René
AU - Hochman, Michael
PY - 2010/7
Y1 - 2010/7
N2 - We exhibit Lipschitz (and hence Hölder) potentials on the full shift {0,1}N such that the associated Gibbs measures fail to converge as the temperature goes to zero. Thus there are "exponentially decaying" interactions on the configuration space {0,1}Z for which the zero-temperature limit of the associated Gibbs measures does not exist. In higher dimension, namely on the configuration space {0,1}Zd, d ≥ 3, we show that this non-convergence behavior can occur for the equilibrium states of finite-range interactions, that is, for locally constant potentials.
AB - We exhibit Lipschitz (and hence Hölder) potentials on the full shift {0,1}N such that the associated Gibbs measures fail to converge as the temperature goes to zero. Thus there are "exponentially decaying" interactions on the configuration space {0,1}Z for which the zero-temperature limit of the associated Gibbs measures does not exist. In higher dimension, namely on the configuration space {0,1}Zd, d ≥ 3, we show that this non-convergence behavior can occur for the equilibrium states of finite-range interactions, that is, for locally constant potentials.
UR - http://www.scopus.com/inward/record.url?scp=77952424179&partnerID=8YFLogxK
U2 - 10.1007/s00220-010-0997-8
DO - 10.1007/s00220-010-0997-8
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AN - SCOPUS:77952424179
SN - 0010-3616
VL - 297
SP - 265
EP - 281
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 1
ER -