Tensor network simulation for the frustrated $J_1$-$J_2$ Ising model on the square lattice

Abstract

By using extensive tensor network calculations, we map out the phase diagram of the frustrated $J_1$-$J_2$ Ising model on the square lattice. In particular, we focus on the cases with controversy in the phase diagram, especially the stripe transition in the regime $g=|J_2/J_1|>\frac{1}{2}$, $(J_2>0,J_1<0)$. While recent studies claimed that the phase transition is of first order when $\frac{1}{2}<g<g^{\ast }$ (with the smallest $g^{\ast }$ being $0.67$), our simulations suggest that if there is such a first-order region, it is smaller than those found in earlier studies by other methods. Combining with the analysis of critical properties, we provide evidence that the classical $J_1$-$J_2$ model evolves continuously from two decoupled Ising models ($g\to \infty$ with central charge $c=1$) to a point belonging to the tricritical Ising universality class (with $c=0.7$) as $g$ decreases to $g^{\ast }\simeq 0.54$.

7 pages, 6 figures, 2 tables

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Cited by in corpus (15)

• Metastable states in the J1-J2 Ising model
• Weak first-order phase transitions in the frustrated square lattice J1-J2 classical Ising model
• Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm
• Universal scaling of Klein bottle entropy near conformal critical points
• Extracting the Luttinger parameter from a single wave function
• Non-monotonic behavior of the Binder Parameter in the discrete spin systems
• Phase determination with and without deep learning
• Tensor network simulations for nonorientable surfaces
• Initial tensor construction and dependence of the tensor renormalization group on initial tensors
• Free energy and metastable states in the square-lattice $J_1$-$J_2$ Ising model
• Tensor network renormalization approach to antiferromagnetic 6-state clock model on the Union Jack lattice
• Comments on the minimal training set for CNN: a case study of the frustrated $J_1$-$J_2$ Ising model on the square lattice
• Frustrated Ising model on the honeycomb lattice: Metastability and universality
• Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices
• Two-dimensional $J_1$-$J_2$ clock model: Enhanced symmetries, emergent orders, and Landau-incompatible transitions