First-order transition and marginal critical behavior in a novel 2D frustrated Ising model

Authors: Christophe Chatelain (LPCT)

Phys. Rev. E 111, 024109 (2024)
arXiv: 2410.01460v1 - DOI (cond-mat.stat-mech)

Abstract: The phase diagram of a novel 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 anti-ferromagnetic Ising replicas coupled by non-local spin-spin interactions, designed in such a way that the continuum limit matches that of the still debated J1 -J2 model and induces a marginal critical behavior. Our model has the advantage of having more symmetries than the J1 -J2 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 J1 -J2 model but not with recent studies with Tensor-Network techniques.

Submitted to arXiv on 02 Oct. 2024

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