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Higuchi Model

The Higuchi model is a simplified model of liquid crystal phase transitions, often used for numerical simulations to study the dynamics of the order parameter.
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The statement of the theorem

Let ψ(x,t)\psi(\mathbf{x}, t) be the order parameter field, and let α\alpha and β\beta be coefficients. The dynamics are governed by the relaxation equation:\n∂ψ∂t=−ΓδFδψ+ξ(x,t)\frac{\partial \psi}{\partial t} = -\Gamma \frac{\delta F}{\delta \psi} + \xi(\mathbf{x}, t)\nwhere the free energy functional FF is defined as:\nF[ψ]=∫Ω[a(T−Tc)ψ2+bψ4+c2∣∇ψ∣2]d3xF[\psi] = \int_{\Omega} \left[ a(T - T_c) \psi^2 + b \psi^4 + \frac{c}{2} |\nabla \psi|^2 \right] d^3x\nand ξ(x,t)\xi(\mathbf{x}, t) is a thermal noise term.
Source: Wikipedia