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首页> 外文期刊>Journal of statistical mechanics: Theory and Experiment >PAPER: Classical statistical mechanics, equilibrium and non-equilibrium Order-disorder transitions in lattice gases with annealed reactive constraints
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PAPER: Classical statistical mechanics, equilibrium and non-equilibrium Order-disorder transitions in lattice gases with annealed reactive constraints

机译：纸质：晶格气体的古典统计力学，平衡和非平衡秩序转变，退火反应约束

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摘要

We study equilibrium properties of catalytically-activated A + A→? reactions taking place on a lattice of adsorption sites. The particles undergo continuous exchanges with a reservoir maintained at a constant chemical potential μ and react when they appear at the neighbouring sites, provided that some reactive conditions are fulfilled. We model the latter in two different ways: in the Model I some fraction p of the bonds connecting neighbouring sites possesses special catalytic properties such that any two As appearing on the sites connected by such a bond instantaneously react and desorb. In the Model II some fraction p of the adsorption sites possesses such properties and neighbouring particles react if at least one of them resides on a catalytic site. For the case of annealed disorder in the distribution of the catalyst, which is tantamount to the situation when the reaction may take place at any point on the lattice but happens with a finite probability p, we provide an exact solution for both models for the interior of an infinitely large Cayley tree—the so-called Bethe lattice. We show that both models exhibit a rich critical behaviour: for the annealed Model I it is characterised by a transition into an ordered state and a re-entrant transition into a disordered phase, which both are continuous. For the annealed Model II, which represents a rather exotic model of statistical mechanics in which interactions of any particle with its environment have a peculiar Boolean form, the transition to an ordered state is always continuous, while the re-entrant transition into the disordered phase may be either continuous or discontinuous, depending on the value of p.
机译：我们研究催化活化A→→→何种平衡性质？在吸附位点的晶格上进行的反应。颗粒与储存器保持连续交换，储存器保持在恒定的化学电位μ，并且当它们出现在相邻位点时反应，就提供了一些反应性条件。我们以两种不同的方式模型：在模型中，连接相邻位点的粘合的一些馏分P具有特殊的催化性质，使得任何两个都出现在通过这种粘合的位点上瞬间反应和解吸。在模型II中，吸附位点的一些馏分P具有这种性质，并且如果其中至少一个在催化位点上存在，则相邻的颗粒反应。对于催化剂分布的退火疾病的情况，这在晶格的任何点处发生反应但随着有限概率P发生时的情况而异，但是，我们为内部的模型提供了精确的解决方案无限大的凯利树 - 所谓的贝特格子。我们表明，两种模型都表现出丰富的关键行为：对于退火模型I，其特征在于转变为有序状态，并且将再参赛者过渡到无序相位，两者都是连续的。对于退火模型II，这代表了一种相当异国统计力学模型，其中任何颗粒与其环境的任何颗粒的相互作用具有特殊的布尔形式，转换到有序状态始终是连续的，而重新进入过渡到无序相可以是连续的或不连续的，具体取决于p的值。

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