Tensor network simulation for the frustrated 
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 Ising model on the square lattice

Li, Hong; Yang, Liping

doi:10.1103/physreve.104.024118

Cited by 21 publications

(2 citation statements)

References 53 publications

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“…In the case of the square lattice-typically free from frustration in the conventional Ising model-a superantiferromagnetic ground state (collinear order) appears when the antiferromagnetic next-nearest-neighbor interaction surpasses half of the nearest-neighbor interaction in magnitude (|R| > 1/2 with R = J 2 /J 1 ) [19,20]. It is generally accepted that the phase transition into the ferromagnetic or antiferromagnetic phase is continuous and belongs to the two-dimensional Ising universality class [20][21][22]. In the phase transition into the collinear super-antiferromagnetic phase, on the other hand, tricriticality has been proposed: the phase transition is first-order for 1/2 < |R| < R * while it is continuous with the weak Ashkin-Teller universality beyond the tricritical point (|R| > R * ) [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo study of frustrated Ising model with nearest- and next-nearest-neighbor interactions in generalized triangular lattices

Jang,

2024

J. Stat. Mech.

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We investigate the frustrated J 1–J 2 Ising model with nearest-neighbor interaction J 1 and next-nearest-neighbor interaction J 2 in two kinds of generalized triangular lattices (GTLs) employing the Wang–Landau Monte Carlo method and finite-size scaling analysis. In the first GTL (GTL1), featuring anisotropic properties, we identify three kinds of super-antiferromagnetic ground states with stripe structures. Meanwhile, in the second GTL (GTL2), which is non-regular in next-nearest-neighbor interaction, the ferrimagnetic 3×3 and two kinds of partial spin liquid (PSL) ground states are observed. We confirm that residual entropy is proportional to the number of spins in the PSL ground states. Additionally, we construct finite-temperature phase diagrams for ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. In GTL1, the transition into the ferromagnetic phase is continuous, contrasting with the first-order transition into the stripe phase. In GTL2, the critical temperature into the ferromagnetic ground state decreases as antiferromagnetic next-nearest-neighbor interaction intensifies until it meets the 3×3 phase boundary. For intermediate values of the next-nearest-neighbor interaction, two successive transitions emerge: one from the paramagnetic phase to the ferromagnetic phase, followed by the other transition from the ferromagnetic phase to the 3×3 phase.

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Section: Introductionmentioning

confidence: 99%

Monte Carlo study of frustrated Ising model with nearest- and next-nearest-neighbor interactions in generalized triangular lattices

Jang,

2024

J. Stat. Mech.

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“…This socalled Klein bottle entropy only depends on conformal data (e.g., modular S matrix for rational CFTs [16][17][18][19][20][21] and the compactification radius for compactified boson CFTs [22]) and can be efficiently computed with various numerical methods, making it a competitive tool for characterizing 2D CFTs in numerics (see Refs. [23][24][25]).…”

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confidence: 99%

Universal Scaling of Klein Bottle Entropy near Conformal Critical Points

et al. 2023

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We show that the Klein bottle entropy [H.-H. Tu, Phys. Rev. Lett. 119, 261603 (2017)] for conformal field theories perturbed by a relevant operator is a universal function of the dimensionless coupling constant. The universal scaling of the Klein bottle entropy near criticality provides an efficient approach to extract the scaling dimension of lattice operators via data collapse. As paradigmatic examples, we validate the universal scaling of the Klein bottle entropy for Ising and Z 3 parafermion conformal field theories with various perturbations using numerical simulation with continuous matrix product operator approach.

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