Self-avoiding tethered membranes at the tricritical point

Abstract The scaling properties of self-avoiding tethered membranes at the tricritical point (Θ-point) are studied by perturbative renormalization group methods. To treat the 3-body repulsive interaction (known to be relevant for polymers), new analytical and numerical tools are developed and applied to 1-loop calculations. These techniques are a prerequisite to higher-order calculations for self-avoiding membranes. The crossover between the 3-body interaction and the modified 2-body interaction, attractive at long range, is studied through a new double ϵ-expansion. It is shown that the latter interaction is relevant for 2-dimensional membranes at the Θ-point.