Analytic continuation and appearance of a new phase forn<1inn-component (φ→2)2field theory

We study the analytic continuation of the renormalized (φ${\to }^2$ ${)}^2$ field theory in the presence of a magnetic field H as a function of n, the number of components of the field φ→, to all real n≥0. We focus our attention at low temperatures (T<$T_c$) for dimensionality d in the range 2<d≤4. We show that while for n≥1 one can reach the limit H→0 below $T_c$ without encountering any singularity in the analytic continuation due to n-1 transverse modes, these modes become catastrophic when n is less than unity for all nonzero H lying below some curve AC defined by H=$H_c$(T)>0 for T<$T_c$ in the H-T plane: The theory cannot be analytically continued below AC for n<1. The catastrophe is caused by n as soon as it becomes less than unity. We calculate the form of AC to first order near $T_c$. For n=0, the paramagnetic phase of the theory describes the dilute regime of the polymer solution as expected. However, we argue that the phase below AC must describe a new phase for polymers, and that there must be a transition across AC from a dilute system to the new phase.