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→Scaling laws
是重要的一类关系。
是重要的一类关系。
== Scaling laws ==
== Scaling laws 标度律 ==
The foregoing are scaling relations in classical thermodynamics. In more recent times, in statistical mechanics, the expression "scaling laws" has been taken to refer to the homogeneity of form of the thermodynamic and correlation functions near critical points, and to the resulting relations among the exponents that occur in those functions. There are many excellent references for critical phenomena and the associated scaling laws, among them the superb book by Domb [1] and the historic early review by Fisher [2].
The foregoing are scaling relations in classical thermodynamics. In more recent times, in statistical mechanics, the expression "scaling laws" has been taken to refer to the homogeneity of form of the thermodynamic and correlation functions near critical points, and to the resulting relations among the exponents that occur in those functions. There are many excellent references for critical phenomena and the associated scaling laws, among them the superb book by Domb [1] and the historic early review by Fisher [2].
引言交代了经典热力学语境下的标度关系。在其后发展出的统计力学中，“标度律”一词指代热力学函数和相关函数在临界点附近的齐次形式，以及这些函数中指数之间的关系。
Near the Curie point (critical point) of a ferromagnet, which occurs
Near the Curie point (critical point) of a ferromagnet, which occurs
H = M\mid M\mid ^{\delta-1} j(t/\mid M\mid
H = M\mid M\mid ^{\delta-1} j(t/\mid M\mid
^{1/\beta}) </math>
^{1/\beta}) </math>
{{NumBlk|:|<math>H = M\mid M\mid ^{\delta-1} j(t/\mid M\mid
当<math>t = T/T_c-1\ ,</math>时，铁磁物质临近居里点（临界点），磁场强度<math>H\ ,</math>，磁化强度<math>M\ ,</math>和<math>t = T/T_c-1\ ,</math>满足{{NumBlk|:|<math>H = M\mid M\mid ^{\delta-1} j(t/\mid M\mid
^{1/\beta})</math>|{{EquationRef|7}}}}
^{1/\beta})</math>|{{EquationRef|7}}}}
{{NumBlk|:|<math>\gamma =
{{NumBlk|:|<math>\gamma =
\beta(\delta-1). </math>|{{EquationRef|8}}}}
\beta(\delta-1). </math>|{{EquationRef|8}}}}
Equations ({{EquationNote|7}}) and
Equations ({{EquationNote|7}}) and