My encounters with Alex Muller and the perovskites

TL;DR

This paper reflects on personal and scientific interactions with Alex Muller, focusing on the complex critical behaviors of cubic perovskites undergoing phase transitions, revealing distinct universality classes for different transition types.

Contribution

It identifies two distinct universality classes for phase transitions in cubic perovskites, based on stress-induced symmetry changes, supported by recent theoretical and experimental insights.

Findings

Cubic to trigonal transition exhibits tetracritical phase diagram with cubic exponents.

Cubic to tetragonal transition shows a bicritical phase diagram evolving into a triple point.

Effective critical exponents should be measured near criticality to test these universality classes.

Abstract

This paper is dedicated to the memory of Professor K. Alex Muller. After describing our personal and scientific encounters since 1974, I concentrate on the many puzzles whinch appeared in our discussions and collaborations, involving the interplay between theory and experiments on the critical behavior of cubic perovskites which undergo (second or first) order transitions to a lower symmetry phases (trigonal or tetragonal). The conclusion, reached only very recently, is that (although beginning with the same cubic symmetry) the two types of transitions belong to two distinct universality classes: under [100] stress, the cubic to trigonal transition exhibits a tetracritical phase diagram, with cubic exponents, while the cubic to tetragonal transition exhibit an intermediate bicritical phase diagram, but asymptotically the bicritical point turns into a triple point, with three first order lines. To test these conclusions, it is suggested to measure the effective critical exponents as the temperature approaches criticality.