Editing Critical exponents
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==Reduced distance: <math>\epsilon</math>== | ==Reduced distance: <math>\epsilon</math>== | ||
<math>\epsilon</math> is the reduced distance from the critical [[temperature]], i.e. | <math>\epsilon</math> is the reduced distance from the critical [[temperature]], i.e. | ||
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:<math>\left. m\right. = m_0 \epsilon^\beta</math> | :<math>\left. m\right. = m_0 \epsilon^\beta</math> | ||
Theoretically one has <math>\beta =0.32653(10)</math><ref name="Campostrini2002"> </ref> for the | Theoretically one has <math>\beta =0.32653(10)</math><ref name="Campostrini2002"> </ref> for the three dimensional Ising model, and <math>\beta = 0.3485(2)</math><ref name="Campostrini2001"> </ref> for the three-dimensional XY universality class. | ||
==Susceptibility exponent: <math>\gamma</math>== | ==Susceptibility exponent: <math>\gamma</math>== | ||
[[Susceptibility]] | [[Susceptibility]] | ||
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:<math>\left. \chi \right. = \chi_0 \epsilon^{-\gamma}</math> | :<math>\left. \chi \right. = \chi_0 \epsilon^{-\gamma}</math> | ||
Theoretically one has <math>\gamma = 1.2373(2)</math><ref name="Campostrini2002"> </ref> for the | Theoretically one has <math>\gamma = 1.2373(2)</math><ref name="Campostrini2002"> </ref> for the three dimensional Ising model, and <math>\gamma = 1.3177(5)</math><ref name="Campostrini2001"> </ref> for the three-dimensional XY universality class. | ||
==Correlation length== | ==Correlation length== | ||
:<math>\left. \xi \right.= \xi_0 \epsilon^{-\nu}</math> | :<math>\left. \xi \right.= \xi_0 \epsilon^{-\nu}</math> | ||
Theoretically one has <math>\nu = 0.63012(16)</math><ref name="Campostrini2002"> </ref> for the | Theoretically one has <math>\nu = 0.63012(16)</math><ref name="Campostrini2002"> </ref> for the three dimensional Ising model, and <math>\nu = 0.67155(27)</math><ref name="Campostrini2001"> </ref> for the three-dimensional XY universality class. | ||
==Inequalities== | ==Inequalities== | ||
====Fisher inequality==== | ====Fisher inequality==== | ||
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where <math>\epsilon</math> is 2/3 for the [[Van der Waals equation of state]], and is usually 0.75 to 0.8. | where <math>\epsilon</math> is 2/3 for the [[Van der Waals equation of state]], and is usually 0.75 to 0.8. | ||
==See also== | |||
*[[Universality classes]] | |||
==References== | ==References== | ||
<references/> | <references/> | ||
[[category: statistical mechanics]] | [[category: statistical mechanics]] |