Induced phase transitions and spontaneous symmetry breaking based on the renormalized Ginzburg-Landau theory

TL;DR

This paper theoretically investigates phase transitions and symmetry breaking using renormalized Ginzburg-Landau theory, highlighting non-universal behaviors and dimensional effects in critical phenomena.

Contribution

It introduces a renormalized Ginzburg-Landau framework that accounts for residual effects and simplifies analysis across different dimensions.

Findings

Non-monotonic relationship between critical temperature and dimensionality

Enhanced or vanished specific heat jump in complex superconductors

Complex thermodynamic expressions in 1D, simplified in 2D and 3D

Abstract

In this study, we present theoretical investigations of phase transitions and critical phenomena in materials through the lens of second-order Ginzburg-Landau theory, in conjunction with considerations of symmetry groups and thermal fluctuations. By addressing the residual effects after a renormalization process, a small number of macroscopic degrees of freedom can effectively replace the infinite number of microscopic degrees of freedom, emphasizing the significant role of dimensionality and the intrinsic characteristics of the system in understanding and analyzing transitions. We highlight several non-universal characteristics of continuous phase transitions near the transition temperature, including the non-monotonic relationship between the critical temperature and dimensionality, as well as the enhancement or disappearance of the specific heat jump in complex superconductors. While the resulting expressions for thermodynamic quantities are complex for one-dimensional systems, obeying Mermin-Wagner's theorem, they are considerably simplified for two-dimensional and three-dimensional systems.