Mean field and exact results for structural phase transitions in one-dimensional and very anisotropic two-dimensional and three-dimensional systems

This paper extends our previous theoretical description of one-dimensional structural phase transitions to two-and three-dimensional systems. Our model has relevance to transitions in ferroelectrics, to highly anisotropic organic and polymeric materials, and possibly to current discussions of nonlinear quantum field theories (following from the analogy between functional integral representations of statistical-mechanical partition functions for continuous fields, and Feynman path-integral formulation of quantum mechanics).