Order of superconductive phase transition

Abstract

On the occasion of Reinhard Folk's 60th birthday, I give a brief review of the theoretical progress in understanding the critical properties of superconductors. I point out the theoretical difficulties in finding a second-order transition in the Ginzburg-Landau Model with O(N )-symmetry in 4 − ε Dimensions, and the success in predicting the existence and location of a tricritical point with the help of a dual disorder theory.

Special Bäcklund transformations and nonlinear superpositions for the non-integrable phi4field model

“…It is well known that the introduction of the φ 4 field in gauge field theory is necessary to solve the nonzero mass problem of the non-Abelian gauge fields. The φ 4 field is significant not only because of its fundamental status in field theory [1] but also because of its wide applications in many other branches of physics and other scientific fields [2][3][4][5][6]. For instance, in statistical mechanics, the φ 4 field can be used to provide an exact expression for the configuration entropy as a function of potential energy and magnetization [2].…”