Destruction of first-order transitions by symmetry-breaking fields

Abstract

Various physical systems with Hamiltonians of cubic and lower symmetry are predicted classically to exhibit second-order phase transitions but known to yield first-order transitions within the renormalization-group approach either (a) because no appropriate "stable" fixed point exists, or (b) because the stable fixed point is not physically accessible. [MnO seems to be an example of (a).] This situation is discussed under circumstances where imposition of a further symmetry-beaking field, $g\gg 1$, restores a continuous transition. Two possible types of phase diagram are identified for $g\to 0$, either (i) without or (ii) with tricritical points. Renormalization-group trajectory calculations for examples of (b), namely a cubic Hamiltonian under a quadratic anisotropy field, are presented: tricritical points are found and a universal amplitude ratio governing their location is calculated to first order in $\epsilon =4-d$.