Composition-tuned smeared phase transitions

TL;DR

This paper investigates smeared phase transitions in substitutional alloys, revealing how local ordering persists across compositions and deriving the behavior of the order parameter using fluctuation theory, supported by simulations and experimental discussion.

Contribution

It introduces a theoretical framework for understanding smeared phase transitions in alloys, including composition dependence and tail behavior, validated by simulations.

Findings

Ordered phase extends over all compositions below x=1

Derived composition dependence of the order parameter

Confirmed results with computer simulations

Abstract

Phase transitions in random systems are smeared if individual spatial regions can order independently of the bulk system. In this paper, we study such smeared phase transitions (both classical and quantum) in substitutional alloys A$_{1-x}$B$_x$ that can be tuned from an ordered phase at composition $x=0$ to a disordered phase at $x=1$. We show that the ordered phase develops a pronounced tail that extends over all compositions $x<1$. Using optimal fluctuation theory, we derive the composition dependence of the order parameter and other quantities in the tail of the smeared phase transition. We also compare our results to computer simulations of a toy model, and we discuss experiments.