trees
two
spin values
solution
true
model
article
translation invariant
values
problem
invariants
splitting Gibbs measures
2017-06
We consider models with four competing interactions (external field, nearest neighbor, second neighbor, and three neighbors) and an uncountable set [0, 1] of spin values on the Cayley tree of order two. We reduce the problem of describing the splitting Gibbs measures of the model to the problem of analyzing solutions of a nonlinear integral equation and study some particular cases for Ising and Potts models. We also show that periodic Gibbs measures for the given models either are translation invariant or have the period two. We present examples where periodic Gibbs measures with the period two are not unique.
particular case
period two
integral equations
example
Gibbs measures
Ising
articles
cases
2022-01-01T18:41
https://doi.org/10.1134/s0040577917060095
https://scigraph.springernature.com/explorer/license/
Four competing interactions for models with an uncountable set of spin values on a Cayley tree
2017-06-01
uncountable set
910-923
interaction
equations
set
Cayley tree
order two
nonlinear integral equations
periodic Gibbs measures
measures
Potts model
en
Haydarov
F. H.
Physical Sciences
Institute of Mathematics and Information Technologies, Tashkent, Uzbekistan
Institute of Mathematics and Information Technologies, Tashkent, Uzbekistan
dimensions_id
pub.1090321667
Mathematical Sciences
191
3
Theoretical and Mathematical Physics
Pleiades Publishing
2305-3135
0040-5779
Rozikov
U. A.
doi
10.1134/s0040577917060095
Springer Nature - SN SciGraph project
National University of Uzbekistan, Tashkent, Uzbekistan
National University of Uzbekistan, Tashkent, Uzbekistan