查看“︁临界指数”︁的源代码

'''临界指数'''（{{lang-en|critical exponent}}）是[[物理学]]中用来描述物理量在[[臨界點 (熱力學)|临界点]]附近行为的指数。尽管没有得到严格证明，实验表明临界指数具有普适性，与具体的物理系统无关，仅和系统维度、关联长度与[[自旋]]维度有关。

对于四维及以上的系统，可以通过[[平均场理论]]计算得到临界指数。但对于低维系统而言平均场理论不再适用，需使用[[重整化群]]方法进行研究。

== 定义 ==
假设[[相变]]出现在临界温度{{math|''T''<sub>c</sub>}}处。为研究临界温度附近物理量 {{math|''f''}} 的行为，我们引入[[约化温度]]
:<math>\tau := \frac{T-T_\mathrm{c}}{T_\mathrm{c}}</math>

相变即发生于约化温度为0时。于是，可以定义临界指数<math>k</math>:

:<math>k \, \stackrel{\text{def}}{=} \, \lim_{\tau \to 0}\frac{\log |f(\tau)| }{\log |\tau|}</math>

相应的幂律关系为
:<math> f(\tau) \propto \tau^k \,, \quad \tau\approx 0 </math>

这代表了{{math|''τ'' → 0}}时函数{{math|''f''(''τ'')}}的渐近行为。更加普遍地，我们有
:<math>f(\tau)=A \tau^k \left(1+b\tau ^{k_1} + \cdots\right) </math>

== 参考文献 ==
* Hagen Kleinert and Verena Schulte-Frohlinde, ''[http://www.physik.fu-berlin.de/~kleinert/b8 Critical Properties of φ<sup>4</sup>-Theories]{{Wayback|url=http://www.physik.fu-berlin.de/~kleinert/b8 |date=20080629214319 }}'', [https://web.archive.org/web/20080226151023/http://www.worldscibooks.com/physics/4733.html World Scientific (Singapore, 2001)]; Paperback {{ISBN|981-02-4658-7}} 
* Toda, M., Kubo, R., N. Saito, ''Statistical Physics I'', Springer-Verlag (Berlin, 1983); Hardcover {{ISBN|3-540-11460-2}}
* J.M.Yeomans, ''Statistical Mechanics of Phase Transitions'', Oxford Clarendon Press
* [[H. Eugene Stanley|H. E. Stanley]] ''Introduction to Phase Transitions and Critical Phenomena'', Oxford University Press, 1971
* A. Bunde and [[Shlomo Havlin|S. Havlin]] (editors), ''[http://havlin.biu.ac.il/Shlomo%20Havlin%20books_f_in_s.php Fractals in Science]{{Wayback|url=http://havlin.biu.ac.il/Shlomo%20Havlin%20books_f_in_s.php |date=20201001025131 }}'', Springer, 1995
* A. Bunde and [[Shlomo Havlin|S. Havlin]] (editors), ''[http://havlin.biu.ac.il/Shlomo%20Havlin%20books_fds.php Fractals and Disordered Systems]{{Wayback|url=http://havlin.biu.ac.il/Shlomo%20Havlin%20books_fds.php |date=20201014022328 }}'', Springer, 1996
* [https://web.archive.org/web/20160204235430/http://www.sklogwiki.org/SklogWiki/index.php/Universality_classes Universality classes] from Sklogwiki
* Zinn-Justin, Jean (2002). ''Quantum field theory and critical phenomena'', Oxford, Clarendon Press (2002), {{ISBN|0-19-850923-5}} 
* Zinn-Justin, J. (2010). [http://www.scholarpedia.org/article/Critical_Phenomena:_field_theoretical_approach "Critical phenomena: field theoretical approach"]{{Wayback|url=http://www.scholarpedia.org/article/Critical_Phenomena:_field_theoretical_approach |date=20201204065902 }} Scholarpedia article Scholarpedia, 5(5):8346.
* F. Leonard and B. Delamotte ''Critical exponents can be different on the two sides of a transition: A generic mechanism'' https://arxiv.org/abs/1508.07852{{Wayback|url=https://arxiv.org/abs/1508.07852 |date=20200806073445 }}

[[Category:相变]]]
[[Category:重整化群]]
[[Category:临界现象]]