更改

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>

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

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>以及 <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}}}}

^{1/\beta}</math> of degree <math>\beta \delta\ .</math>  The scaling function <math>j(x)</math> vanishes proportionally to <math>x+b</math> as <math>x</math> approaches <math>-b\ ,</math> with <math>b</math> a positive constant; it diverges proportionally to <math>x^{\beta(\delta-1)}</math> as <math>x\rightarrow \infty\ ;</math> and <math>j(0) = c\ ,</math> another positive constant (Fig. 1). Although ({{EquationNote|7}}) is confined to the immediate neighborhood of the critical point <math>(t, M, H</math> all near 0), the scaling variable <math>x = t/\mid M\mid ^{1/\beta}</math> nevertheless traverses the infinite range <math>-b < x < \infty\ .</math>

^{1/\beta}</math> of degree <math>\beta \delta\ .</math>  The scaling function <math>j(x)</math> vanishes proportionally to <math>x+b</math> as <math>x</math> approaches <math>-b\ ,</math> with <math>b</math> a positive constant; it diverges proportionally to <math>x^{\beta(\delta-1)}</math> as <math>x\rightarrow \infty\ ;</math> and <math>j(0) = c\ ,</math> another positive constant (Fig. 1). Although ({{EquationNote|7}}) is confined to the immediate neighborhood of the critical point <math>(t, M, H</math> all near 0), the scaling variable <math>x = t/\mid M\mid ^{1/\beta}</math> nevertheless traverses the infinite range <math>-b < x < \infty\ .</math>

其中<math>j(x)</math>是“标度”函数，<math>\beta</math>和<math>\delta</math>是临界点指数。因此由({{EquationNote|2}})和({{EquationNote|7}})，当铁磁物质趋近于临界点时<math>(H\rightarrow 0</math>且<math>t\rightarrow 0)\ ,</math>，<math>\mid H\mid</math>是 <math> t </math> 和<math>\mid M\mid

其中<math>j(x)</math>是“标度”函数，<math>\beta</math>和<math>\delta</math>是临界点指数。因此由({{EquationNote|2}})和({{EquationNote|7}})，当铁磁物质趋近于临界点时<math>(H\rightarrow 0</math>且<math>t\rightarrow 0)\ </math>，<math>\mid H\mid</math>是 <math> t </math> 和<math>\mid M\mid

^{1/\beta}</math>的<math>\beta \delta\ </math>次齐次函数。当<math>x</math>趋近于<math>-b\</math>（正常数）时，标度函数<math>j(x)</math>趋近于零；当<math>x\rightarrow \infty\ ;</math>时，它发散至<math>x^{\beta(\delta-1)}</math>，且<math>j(0) = c\ </math>（正常数）（如图一）。尽管({{EquationNote|7}})局限在临界点<math>(t, M, H</math>都接近零）附近的极小范围内，但标度变量<math>x = t/\mid M\mid ^{1/\beta}</math>却遍历<math>-b < x < \infty\</math>的无穷范围。

^{1/\beta}</math> 的<math>\beta \delta\ </math>次齐次函数。当<math> x </math>趋近于<math>-b\</math>（正常数）时，标度函数<math>j(x)</math>趋近于零；当<math>x\rightarrow \infty\ </math>时，它依<math>x^{\beta(\delta-1)}</math>成比例发散（如图一），且<math>j(0) = c\ </math>（正常数）。尽管({{EquationNote|7}})局限在临界点<math>(t, M, H</math>都接近零）附近的极小范围内，但标度变量<math>x = t/\mid M\mid ^{1/\beta}</math>却遍历<math>-b < x < \infty\</math>的无穷范围。

[[Image:scaling_laws_widom_nocaption_Fig1.png|thumb|300px|right|Scaling function  

[[Image:scaling_laws_widom_nocaption_Fig1.png|thumb|300px|right|Scaling function  

({{EquationNote|8}}) are examples of scaling laws, Eq.({{EquationNote|7}}) being a statement of homogeneity and the exponent relation ({{EquationNote|8}}) a consequence of that homogeneity.

({{EquationNote|8}}) are examples of scaling laws, Eq.({{EquationNote|7}}) being a statement of homogeneity and the exponent relation ({{EquationNote|8}}) a consequence of that homogeneity.

当<math>\mid H\mid = 0+</math>且<math>t<0\ ,</math><math>M</math>是自发磁化，从({{EquationNote|7}})可得<math>\mid M\mid = (-\frac{t}{b})^\beta\ ,</math>其中<math>\beta</math>是这一临界指数的常用符号。在临界等温线<math>(t=0)\ ,</math>当<math>M\rightarrow 0</math>时，我们有<math>H \sim cM\mid

当<math>\mid H\mid = 0+</math>且<math>t<0\ </math>，<math>M</math>是自发磁化率，由({{EquationNote|7}})可得<math>\mid M\mid = (-\frac{t}{b})^\beta\ </math>，其中<math>\beta</math>对应这一临界指数。在临界等温线<math>(t=0)\ </math>，当<math>M\rightarrow 0</math>时，我们有<math>H \sim cM\mid

M\mid ^{\delta-1}\ ,</math>其中<math>\delta</math>是这一临界指数的常用符号。由前文中<math>j(x)</math>的第一个性质和式({{EquationNote|7}})，或可以计算磁化率<math>(\partial

M\mid ^{\delta-1}\ </math>，其中<math>\delta</math>为此时的临界指数。由前文中<math>j(x)</math>的第一个性质和({{EquationNote|7}})式，我们可以计算磁化率<math>(\partial

M/\partial H)_T\ ,</math>，它在<math>\mid

M/\partial H)_T\ </math>，它在<math>\mid

H\mid = 0+</math>且<math>t<0</math>以及在<math>H=0</math>且<math>t>0</math>时成比例发散至<math>\mid t\mid ^{-\beta(\delta-1)}\</math>（尽管系数不同）。磁化率指数的常用符号是<math>\gamma\ ,</math>因此有{{NumBlk|:|<math>\gamma =

H\mid = 0+</math>且<math>t<0</math>，以及在<math>H=0</math>且<math>t>0</math>时依<math>\mid t\mid ^{-\beta(\delta-1)}\</math>成比例发散（尽管系数不同）。磁化率指数的常用符号是<math>\gamma\ </math>，因此有{{NumBlk|:|<math>\gamma =

\beta(\delta-1). </math>|{{EquationRef|8}}}}

\beta(\delta-1). </math>|{{EquationRef|8}}}}