First-order transition and marginal critical behavior in a two-dimensional frustrated Ising model with efficient tensor-network implementation.

The phase diagram of a two-dimensional frustrated Ising model with both anti-ferromagnetic and ferromagnetic couplings is studied using tensor network renormalization group techniques. This model can be seen as two antiferromagnetic Ising replicas coupled by nonlocal spin-spin interactions, designed in such a way that the continuum limit matches that of the still-debated J_{1}-J_{2} model and induces a marginal critical behavior. Our model has the advantage of having more symmetries than the J_{1}-J_{2} model and of allowing a more straightforward implementation of tensor network renormalization group algorithms. We demonstrate the existence of two transition lines, featuring both first- and second-order regimes. In the latter, the central charge and the critical exponents are shown to be compatible with the Ashkin-Teller universality class. This picture is consistent with that given by Monte Carlo simulations of the J_{1}-J_{2} model but not with recent studies with tensor network techniques.