Tensor renormalization-group study of the surface critical behavior of a frustrated two-layer Ising model

Abstract Two replicas of a 2D Ising model are coupled by frustrated spin-spin interactions. It is known that this inter-layer coupling is marginal and that the bulk critical behavior belongs to the Ashkin–Teller (AT) universality class, as the J 1 − J 2 Ising model. In this work, the surface critical behavior is studied numerically by tensor renormalization-group calculations. The bond-weight tensor renormalization group algorithm is extended to tackle systems with boundaries. It is observed that the two-fold degeneracy of the surface magnetic scaling dimension of the AT model is lifted in the frustrated two-layer Ising model (F2LIM). The splitting is explained by the breaking of the Z 2 -symmetry under spin reversal of a single Ising replica in the F2LIM. The two distinct surface magnetic scaling dimensions x 1 s and x 2 s of the F2LIM satisfies a simple duality relation x 1 s = 1 / 4 x 2 s .