Critical Behavior of Anisotropic Cubic Systems

Abstract

The critical behavior in zero field above $T_c$ of ferromagnets or ferroelectrics with a Hamiltonian of cubic symmetry is studied, to order ${\epsilon }^2$, by exact renormalization-group techniques in $d=4-\epsilon$ dimensions with $n$-component spins. For $\epsilon =1\mathrm{}$, $n\ge 3$, a crossover from isotropic (Heisenberg) to characteristic cubic behavior occurs, with the new value $2v^C=1+\left[\frac{\mathrm{}(n-1\mathrm{})\mathrm{}}{3n}\right]\epsilon +\left[\frac{\mathrm{}(n-1\mathrm{})\mathrm{}}{324n^3}\right](17\mathrm{}{n}^2+290n-424){\epsilon }^2+O\left({\epsilon }^3\right)$, and cubic symmetry appearing in the four-spin correlation function. Experiments on structural phase transitions are considered briefly.