Quantum Ising model on the frustrated square lattice

Kellermann, N.; Schmidt, M.; Zimmer, F.M.

doi:10.1103/physreve.99.012134

Cited by 30 publications

(25 citation statements)

References 33 publications

(75 reference statements)

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“…As a consequence, the phase transition at g = 0.46 is of continuous type, and belongs to the Ising universal class which we can prove below. The recent work using CMF provides the same conclusion [30]. Now we move to the case of g = 0.55.…”

Section: A Phase Diagram and Physical Quantitiessupporting

confidence: 64%

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

Li,

Yang

2021

Preprint

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By the extensive tensor network algorithms, we provide the phase diagram of the frustrated J1-J2 Ising model on the square lattice. Based on the fine numerical simulations, we discuss the cases with controversy in the phase diagram, especially for the stripe transition in the regime g = |J2/J1| > 1/2, (J2 > 0, J1 < 0). Our simulations suggest that the first-order phase transition may reside in a very narrow parameter region 1/2 < g < g * (g * is much smaller than previous research). Combining with the analysis of critical properties, we find the evidence that the classical J1-J2 model evolves continously from two decoupled Ising models (g → ∞ with central charge c = 1) to a point of tricritical Ising model (with c = 0.7) as g decreases to g * .

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Section: A Phase Diagram and Physical Quantitiessupporting

confidence: 64%

“…In addition, they claimed the pseudo-first-order behavior at g g * . MC simulations with larger system size strengthened their conclusion [29] and recent cluster mean-field (CMF) [30] also mentioned the consistent results.…”

Section: Introductionmentioning

confidence: 61%

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

Li,

Yang

2021

Preprint

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“…In this paper, we investigate the AF J 1 -J 2 Ising model on the bcc lattice within a cluster mean-field (CMF) approach. This method has been used in several recent studies of phase diagrams and thermodynamic quantities of frustrated spin models [5,6,[11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In particular, this framework provided a description of phase transitions for J 1 -J 2 spin models on square [11,23] and honeycomb [6] lattices in very good agreement with recent Monte Carlo results.…”

Section: Introductionsupporting

confidence: 65%

“…Spin models with competing exchange couplings between first (J 1 ) and second (J 2 ) neighbours are a permanent venue to investigate frustration effects on phase transitions. The complex phenomena hosted by J 1 -J 2 spin models has motivated numerous investigations in the past few years [1][2][3][4][5][6][7]. Recently, the thermal phase transitions presented by the antiferromagnetic (AF) J 1 -J 2 Ising model on the body-centered cubic (bcc) lattice has been a relevant subject of debate [1,2].…”

Section: Introductionmentioning

confidence: 99%

The frustrated Ising model on the body-centered cubic lattice

Schmidt,

Kohlrausch,

Zimmer

2021

Preprint

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Recent results for the Ising model with first (J1) and second (J2) neighbour interactions on the body-centered cubic (bcc) lattice suggest that this model can host signatures of strong frustration, including Schottky anomalies and residual entropy, as well as, a spin-liquid-like phase [E. Jurčišinová and M. Jurčišin, Phys. Rev. B, 101 214443 (2020)]. Motivated by these findings, we investigate phase transitions and thermodynamics of this model using a cluster mean-field approach. In this lattice, tuning g = J2/J1 leads to a ground-state transition between antiferromagnetic (AF) and superantiferromagnetic (SAF) phases at the frustration maximum g = 2/3. Although the ordering temperature is reduced as g → 2/3, our findings suggest the absence of any Schottky anomaly and residual entropy, in good agreement with Monte Carlo simulations. We also find a direct transition between AF and SAF phases, ruling out the presence of the spin-liquid-like state. Furthermore, the cluster mean-field outcomes support a scenario with only continuous phase transitions between the paramagnetic state and the low-temperature long-range orders. Therefore, our results indicate the absence of strong frustration effects in the thermodynamics and in the nature of phase transitions, which can be ascribed to the higher dimensionality of the bcc lattice.

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“…Nevertheless, even the value of R * in the latter cases has been a subject of controversy with rather different estimates ranging from the early −1.1 [9] down to the latest −0.67 [16]. The effects of a transverse field [19][20][21] and stacking of the 2D layers in a vertical direction [22,23] on the critical properties the model have also been investigated.…”

Section: Introductionmentioning

confidence: 99%

Critical properties of the frustrated Ising model on a honeycomb lattice: A Monte Carlo study

Žukovič

2021

Preprint

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Critical and in the highly frustrated regime also dynamical properties of the J 1 − J 2 Ising model with competing nearest-neighbor J 1 and second-nearest-neighbor J 2 interactions on a honeycomb lattice are investigated by standard Monte Carlo and parallel tempering simulations. The phase boundary is determined as a function of the coupling ratio for the phase transition between the paramagnetic and ferromagnetic states within R ≡2 the transition remains second-order and complies with the standard Ising universality class. In the highly frustrated regime of R < −0.2 and low temperatures the system tends to freeze to metastable domain states, separated by large energy barriers, which show extremely sluggish dynamics. The resulting huge equilibration and autocorrelation times hinder the analysis of critical properties by using standard Monte Carlo techniques. The parallel tempering approach facilitates much better tunneling through the energy barriers, nevertheless, the convergence to the equilibrium remains beyond the reach even for relatively small system sizes and thus the character of the transition in this region remains to be determined.

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Quantum Ising model on the frustrated square lattice

Cited by 30 publications

References 33 publications

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

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

The frustrated Ising model on the body-centered cubic lattice

Critical properties of the frustrated Ising model on a honeycomb lattice: A Monte Carlo study

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