对于批判性书籍排版和书籍传播的长期订单
Hugo Duminil-Copin1,2, Christophe Garban3, Vincent Tassion4
1Université de Genève, 2-4 rue du Lièvre, 1204 Geneve, Switzerland.
概括
多页书中的统计物理模型表现出不连续的相位过渡,即使是连续过渡的模型. 当页面数量很大时,会出现这种情况,正如Ising模型在三页书中所示的那样.
科学领域:
- 统计物理学的统计物理.
- 数学物理学的数学物理.
- 凝聚物质理论 凝聚物质理论
背景情况:
- 统计物理模型通常在简单的几何上表现出连续的相位过渡.
- 这些模型在复杂或非欧几里德空间上的行为不太清楚.
- 之前的理论研究表明,在这样的系统中,相位过渡特性发生了变化.
研究的目的:
- 在"图书"几何上研究统计物理模型的相位过渡行为 (页面为半平面).
- 为了确定连续相位过渡是否可以在本书的多元体上变为不连续.
- 为了在一本三页的书中专门分析伊辛格模型.
主要方法:
- 统计物理模型的数学分析.
- 在由半平面组成的多重体上研究模型 (书面几何).
- 专注于具有特定合常量的Ising模型.
主要成果:
- 在一个平面上经历连续相位过渡的模型在一本有足够页面的书中表现出不连续的过渡.
- 在一本三页书上的伊辛模型展示了一个不连续的相位过渡.
- 这一发现取决于在页面界面上考虑大的合常量.
结论:
- 空间的几何学显著影响了统计物理学中的相位过渡特性.
- 一个"书本"的多元组可以诱导相变中的不连续性,而相变在更简单的空间中是连续的.
- 结果与重新规范化组和合规场理论的先前理论预测一致,并证实了这些预测.
相关概念视频
Entropy
30.2K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
30.2K
Indeterminate Structure
538
Indeterminate structures refer to structures where internal forces and reactions cannot be determined using only the equations of static equilibrium. Indeterminate structures have more unknown forces and reaction forces than equations of static equilibrium that can be used to determine them. Indeterminate structures are often used in engineering to create complex, efficient, and aesthetically pleasing structures. There are various types of indeterminate structures used in engineering and...
538
The Buckingham Pi Theorem
666
The Buckingham Pi theorem provides a structured method to simplify fluid dynamics problems by reducing complex systems of variables to dimensionless terms.
666
Orders of Magnitude
17.7K
The order of magnitude of a number is the power of 10 that most closely approximates it. Thus, the order of magnitude estimates the scale (or size) of its value. To find the order of magnitude of a number, take the base-10 logarithm of the number and round it to the nearest integer. Then the order of magnitude of the number is simply the resulting power of 10.
The order of magnitude is simply a way of rounding numbers consistently to the nearest power of 10. This makes doing rough mental math...
The order of magnitude is simply a way of rounding numbers consistently to the nearest power of 10. This makes doing rough mental math...
17.7K
Interference: Path Lengths
1.3K
Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
1.3K
¹H NMR: Interpreting Distorted and Overlapping Signals
1.0K
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
1.0K


