order parameter

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Write our partition function by isolating configurations with some particular value of some operator:

Z = \int\!\mathcal{D}\phi \,e^{-S[\phi]} = \int\!d\Phi \int\!\mathcal{D}\phi \Delta \delta( \hat\Phi[\phi] - \Phi ) e^{-S[\phi] }\,.

This defines the free energy:

e^{-\frac{F[\Phi]}{T}} = \int\!\mathcal{D}\phi \Delta \delta( \hat\Phi[\phi] - \Phi ) e^{-S[\phi] }\,.

We may implement the delta function via the method of Lagrange multipliers.

See also

order parameter (Statistical mechanics)

References

[1]

  1. ↑ J. York (1986). "Black-hole thermodynamics and the Euclidean Einstein action". Phys. Rev. D 33: 2092 - 2099. DOI:10.1103/PhysRevD.33.2092. 
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