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The statistical mechanics of 1D and 2D Ginzburg-Landau systems is evaluatedanalytically, via the transfer matrix method, using an expression of the groundstate energy of the quartic anharmonic oscillator in an external field. In the2D case, the critical temperature of the order/disorder phase transition isexpressed as a Lambert function of the inverse inter-chain coupling constant.

The quartic oscillator in an external field and the statistical physics of highly anisotropic solids