In this paper we study the singular limit for critical points of boundary reactions \(\begin{aligned} (-\Delta )^{\frac{1}{2}}u = \frac{1}{\varepsilon }(u-u^3) \quad \text {in } \Omega \subset {\textbf {R}}^n. \end{aligned}\) We show the existence of a \((n-1)\) -rectifiable energy concentration set. Furthermore, we show that the limit of the energy measures can be associated to a stationary, \((n-1)\) -rectifiable varifold supported in the concentration set. This is analogous to a result of Hutchinson and Tonegawa for phase transitions.
