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

TL;DR

This paper analytically investigates the statistical mechanics of low-dimensional Ginzburg-Landau systems using the ground state energy of a quartic oscillator, revealing phase transition properties and critical temperatures.

Contribution

It introduces an analytical approach to study 1D and 2D Ginzburg-Landau systems via the transfer matrix method and quartic oscillator energy expressions, providing new insights into phase transitions.

Findings

Critical temperature expressed as Lambert function of inter-chain coupling

Analytical evaluation of ground state energy for quartic oscillator

Insights into order/disorder phase transition in low-dimensional systems

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.