The quartic oscillator in an external field and the statistical physics of highly anisotropic solids
arXiv:0912.1988
Abstract
The statistical mechanics of 1D and 2D Ginzburg-Landau systems is evaluated analytically, via the transfer matrix method, using an expression of the ground state energy of the quartic anharmonic oscillator in an external field. In the 2D case, the critical temperature of the order/disorder phase transition is expressed as a Lambert function of the inverse inter-chain coupling constant.
13 pages