具有可数自旋值集的 HC 模型的弱周期吉布斯量度

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL Reports on Mathematical Physics Pub Date : 2024-08-01 DOI:10.1016/S0034-4877(24)00057-0

Muhtorjon Makhammadaliev

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引用次数: 0

摘要

本文研究了硬核（HC）模型的弱周期（非周期性）吉布斯量度，该模型具有可数的自旋值集合ℤ和可数的参数集合λi > 0, i∈ ℤ，在阶数k≥2的卡莱树上。对于所考虑的模型，在∑i λi < +∞情况下，对于索引为二的任何正整除数，都能得到弱周期吉布斯度量的完整描述；而在∑i; λi = +∞情况下，则证明不存在弱周期吉布斯度量。此外，在指数为四的正态除数情况下，还发现了弱周期吉布斯量的唯一性条件。此外，在某些条件下，还找到了确保弱周期吉布斯量存在的精确临界值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Weakly periodic gibbs measures for the HC model with a countable set of spin values

In this paper, we study the weakly periodic (nonperiodic) Gibbs measures for the Hard Core (HC) model with a countable set ℤ of spin values and with a countable set of parameters λ_i > 0, i ∈ ℤ, on a Cayley tree of order k ≥ 2. For the considered model in the case ∑_i λ_i < +∞, a complete description of weakly periodic Gibbs measures is obtained for any normal divisor of index two and in the case ∑_i; λ_i = +∞, it is shown that there is no weakly periodic Gibbs measure. Moreover, in the case of a normal divisor of index four the uniqueness conditions for weakly periodic Gibbs measures are found. Further, under certain conditions an exact critical value is found that ensures the existence of weakly periodic Gibbs measures.

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.