First-order transition and marginal critical behavior in a two-dimensional frustrated Ising model with efficient tensor-network implementation
Year: 2025
Type: article
Abstract: 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.
Source: Physical review. E
Author: Christophe Chatelain
Institution: Laboratoire de Physique et Chimie Théoriques
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W4407193236