在XY模型中,具有更高阶项的XY模型中,在不同的普遍性类中任意数量的热诱导相变
1P. J. Šafárik University, Institute of Physics, Faculty of Science, Park Angelinum 9, 041 54 Košice, Slovakia.
Physical review. E
|November 18, 2025
概括
一般化的XY模型表现出多个温度驱动的相位过渡. 这些模型显示了在达到铁磁阶段之前的阴性相级联,过渡类型取决于模型参数.
科学领域:
- 凝聚物质物理学 凝聚物质物理学
- 统计力学 统计力学
- 理论物理 理论物理
背景情况:
- XY模型是统计力学的一个基本模型,通常表现为单相过渡.
- 了解具有多个相位过渡的模型对于探索复杂物质行为至关重要.
研究的目的:
- 提出和研究能够展示任意数量的温度驱动相变的通用XY模型.
- 描述这些新型阶段过渡的性质和普遍性类.
主要方法:
- 通过向标准磁性合添加指数式增加顺序的无形项来构建概括的XY模型.
- 模型参数的系统变化,包括基 q (2, 3, 4, 5) 和相互作用强度.
- 分析相位过渡行为,包括Berezinskii-Kosterlitz-Thouless (BKT) 和非BKT过渡及其相关的普遍性类.
主要成果:
- 对于q=2,3,和4,模型表现出相位过渡的数量等于哈密尔顿数中的项数,通过内马特相向铁磁相过渡.
- 过渡的特点是越来越多的优先旋转方向,属于Ising或三态Potts普遍性类,除了最初的BKT过渡.
- 对于q=5,相位过渡分裂,使有序相数增加到2n_{t}-1,复杂的域结构和排序似乎不遵循标准的普遍性.
结论:
- 一般化的XY模型提供了一个可调的平台,用于研究多个温度驱动的相位过渡.
- 这些转换的性质和普遍性高度依赖于模型的构造,特别是内马特术语的顺序和强度.
- q=5案例揭示了复杂的新兴行为,具有新的有序阶段和过渡,突出了一般化磁模型的丰富性.
相关概念视频
02:31Phase Transitions
22.3K
Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
22.3K
02:38Third Law of Thermodynamics
21.5K
A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
21.5K
02:39Phase Transitions: Melting and Freezing
14.5K
Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
14.5K
02:33Phase Transitions: Sublimation and Deposition
19.6K
Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
19.6K
02:39Phase Transitions: Vaporization and Condensation
20.5K
The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...
20.5K
02:49Second Law of Thermodynamics
26.6K
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
26.6K