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

Abstract

The statistical mechanics of one- and two-dimensional 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 two-dimensional case, the critical temperature of the order–disorder phase transition is expressed as a Lambert function of the inverse inter-chain coupling constant.

Keywords:

• anisotropy
• low-dimensional structures
• phase transitions
• statistical mechanics

Acknowledgements

The author thanks CNCSIS and UEFISCSU for funding the research presented in this paper, through the project IDEI 2008 no. 953. He is also grateful to the (anonymous) referees of this journal, for useful comments and criticism.