•  
  •  
 

Scientific Bulletin of Namangan State University

Abstract

We study weakly periodic Ground States for the model of SOS with competing interactions on the Cayley tree of order two.

First Page

14

Last Page

21

References

[1] K.Preston, Gibbsovskie sostoyaniya na schetnx mnojestvax, Mir, M., 1977. [2] U.A.Rozikov, 2013 Gibbs Measures on Cayley Trees, World Scientific, Hackensack. [3] R.Fernandez, Contour ensembles and the description of Gibbsian probability distributions at low temperature, http://dl.univ-rouen.fr LMRS Persopage Fernandez resucont.html, 1998. [4] U.A.Rozikov and M.M.Rakhmatullaev,“Weakly periodic ground states and Gibbs measures for the Ising model with competing interactions on the Cayley tree,”Theoret. Math. Phys.160, 1292 (2009) [Teor. Mat. Fiz.160, 507 2009)]. [5] M.M.Rakhmatullaev,“Description of weak periodic ground states of Ising model with competing interactions on Cayley tree,”Appl. Math. Inf. Sci.4, 237 (2010). [6] M.M.Rakhmatullaev,“Weakly periodic Gibbs measures and ground states for the Potts model with competing interactions on the Cayley tree,”Theoret. Math. Phys.176, 1236 (2013) [Teor. Mat. Fiz. 176, 477 (2013)].[7] M.M.Rahmatullaev, M.A.Rasulova., Periodic and Weakly Periodic Ground States for the Potts Model with Competing Interactions on the Cayley Tree. Siberian Advances in Mathematics, 2016, Vol. 26, No. 3, pp. 215–229. [8] U.A.Rozikov., Description of limit Gibbs measures for models on Bethe lattices. Siberian Mathematical Journal, Vol. 39, No. 2, 1998 [9] O.Melnikov, R.I.Tyshkevich, V.A.Yemelichev, and V.I.Sarvanov, Lectures on Graph Theory (B.I.Wissenschaftsverlag, Mannheim, 1994) [Lectures on Graph Theory. Textbook (Nauka, Moscow, 1990)].

Erratum

???????

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.