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

TL;DR

This paper investigates a novel 2D frustrated Ising model with mixed couplings, revealing first-order and marginal critical behaviors, and clarifies its relation to the J1-J2 model using advanced tensor-network methods.

Contribution

It introduces a new frustrated Ising model with enhanced symmetries and demonstrates its phase transitions and critical behavior using Tensor-Network Renormalization-Group techniques.

Findings

Identifies two transition lines with first and second-order regimes.

Shows the second-order regime aligns with Ashkin-Teller universality.

Provides insights consistent with Monte Carlo results but not with recent tensor-network studies.

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.