Continuum Quantum Ferromagnets at Finite Temperature and the Quantum Hall Effect

We study finite temperature ( $T$) properties of the continuum quantum field theory of systems with a ferromagnetic ground state. A scaling theory of the $T=0\mathrm{}$ system is discussed carefully, and its consequences for crossovers between different finite $T$ regimes in dimensions 1, 2, and 3 are described. The results are compared with recent NMR measurements of the magnetization of a quantum Hall system with filling factor $\nu =1\mathrm{}$; we predict that the relaxation rate $1/T_1$ of this system may have a finite $T$ “ferromagnetic coherence peak.”