Quantum effects in an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-component vector model for structural phase transitions

Abstract

The influence of quantum effects on the critical properties of an $n$-component vector model for structural phase transitions is explored. It is shown for $n=1,2, \mathrm{and} \ensuremath{\infty}$ that these effects can suppress the occurrence of a phase transition for all dimensions $d$. This turns out to be of particular relevance for systems where the classical transition temperature almost vanishes (${T}_{c}=0$ represents the displacive limit). We also discuss the critical properties at this limit for $n=\ensuremath{\infty}$ and show that the critical exponents change discontinously.