Description of weakly periodic Gibbs measures for the~Ising model on a~Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 2, pp. 292-302
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We introduce the concept of a weakly periodic Gibbs measure. For the Ising model, we describe a set of such measures corresponding to normal subgroups of indices two and four in the group representation of a Cayley tree. In particular, we prove that for a Cayley tree of order four, there exist critical values $T_{\mathrm{c}}$ of the temperature $T>0$ such that there exist five weakly periodic Gibbs measures for $0$ or $T>T_{\mathrm{cr}}$, three weakly periodic Gibbs measures for $T=T_{\mathrm{c}}$, and one weakly periodic Gibbs measure for $T_{\mathrm{c}}$.
Keywords:
Cayley tree, Gibbs measure, Ising model, weakly periodic measure.
@article{TMF_2008_156_2_a10,
author = {U. A. Rozikov and M. M. Rakhmatullaev},
title = {Description of weakly periodic {Gibbs} measures for {the~Ising} model on {a~Cayley} tree},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {292--302},
publisher = {mathdoc},
volume = {156},
number = {2},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2008_156_2_a10/}
}
TY - JOUR AU - U. A. Rozikov AU - M. M. Rakhmatullaev TI - Description of weakly periodic Gibbs measures for the~Ising model on a~Cayley tree JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2008 SP - 292 EP - 302 VL - 156 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2008_156_2_a10/ LA - ru ID - TMF_2008_156_2_a10 ER -
%0 Journal Article %A U. A. Rozikov %A M. M. Rakhmatullaev %T Description of weakly periodic Gibbs measures for the~Ising model on a~Cayley tree %J Teoretičeskaâ i matematičeskaâ fizika %D 2008 %P 292-302 %V 156 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2008_156_2_a10/ %G ru %F TMF_2008_156_2_a10
U. A. Rozikov; M. M. Rakhmatullaev. Description of weakly periodic Gibbs measures for the~Ising model on a~Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 2, pp. 292-302. http://geodesic.mathdoc.fr/item/TMF_2008_156_2_a10/