New class of Gibbs measures for two-state hard-core model on a Cayley tree-Reference-Cited by-同舟云学术

New class of Gibbs measures for two-state hard-core model on a Cayley tree

Published:2023-10-20 Issue:04 Volume:26 Page:
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

Khakimov R. M.¹²,Makhammadaliev M. T.¹²,Haydarov F. H.¹³⁴⁵^ORCID

Affiliation:

1. Institute of Mathematics, 9, University Street, Tashkent 100174, Uzbekistan

2. Namangan State University, Uychi Street, Namangan 716019, Uzbekistan

3. New Uzbekistan University, 54, Mustaqillik Avenue, Tashkent 100007, Uzbekistan

4. Central Asian University, 264, Milliy Bog Street, Tashkent 111221, Uzbekistan

5. National University of Uzbekistan, University Street, Tashkent 100174, Uzbekistan

Abstract

In this paper, we consider a Hard-Core (HC) model with two spin values on Cayley trees. The conception of alternative Gibbs measure is introduced and translational invariance conditions for alternative Gibbs measures are found. Also, we show that the existence of alternative Gibbs measures which are not translation-invariant. In addition, we study free energy of the model.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025723500248

Reference40 articles.

1. Random surfaces with two-sided constraints: An application of the theory of dominant ground states

2. Gibbs States on Countable Sets

3. New Phase Transitions of the Ising Model on Cayley Trees

4. On Free Energies of the Ising Model on the Cayley Tree

5. Fast mixing for independent sets, colorings, and other models on trees

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