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First Principles of the Classical Mechanics and the Foundations of Statistical Mechanics on the Example of a Disordered Spin System
Journal of Contemporary Physics (Armenian Academy of Sciences) ( IF 0.6 ) Pub Date : 2020-12-03 , DOI: 10.3103/s106833722004009x
A. S. Gevorkyan , V. V. Sahakyan

Abstract

We study the classical multicomponent disordered 3D spin system taking into account the temperature of the medium in the framework of the model of nearest neighbors. The latter allows the 3D problem with a cubic lattice to reduce to the 1D Heisenberg spin glass problem with a random environment. Using the Hamilton equations of motion, a recurrent equation is obtained that connects three spins in successive nodes of 1D lattice, taking into account the influence of a random environment. This equation, together with the corresponding conditions of a local minimum energy in nodes, allows to construct node-by-node a stable spin chains and, accordingly, to calculate all parameters of statistical ensemble from the first principles of classical mechanics, without using any additional assumptions, in particular, the main axiom of statistical mechanics – the equiprobability of statistical states. Using the example of 1D Heisenberg spin glass model, the features of the new approach are studied in detail and the statistical mechanics of the system are constructed without using the standard representation of the partition function (PF).



中文翻译:

以无序自旋系统为例的古典力学的第一原理和统计力学的基础

摘要

我们在最邻近模型的框架内考虑了介质的温度,研究了经典的多组分无序3D自旋系统。后者允许将具有立方晶格的3D问题简化为具有随机环境的1D Heisenberg自旋玻璃问题。使用汉密尔顿运动方程,考虑到随机环境的影响,获得了一个递归方程,该方程将一维晶格的连续节点中的三个自旋连接起来。该方程式与节点中局部最小能量的相应条件一起,允许逐节点构造稳定的自旋链,并因此根据经典力学的第一原理计算统计集合的所有参数,而无需使用任何其他假设,尤其是 统计力学的主要公理–统计状态的等概率。以一维海森堡旋转玻璃模型为例,详细研究了该新方法的特征,并且在不使用分配函数(PF)的标准表示的情况下构造了系统的统计机制。

更新日期:2020-12-03
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