Cluster Monte Carlo dynamics for the antiferromagnetic Ising model on a triangular lattice

Zhang, G. M.; Yang, Cheng-Fu

doi:10.1103/physrevb.50.12546

Cited by 15 publications

(22 citation statements)

References 24 publications

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“…This method was introduced by Kandel et al [12] for the study of frustrated systems. Recently Zhang and Cheng [13] have applied this algorithm to the zero-field TIAFM. We have modified this algorithm to take into account the presence of the staggered field.…”

Section: Cluster Dynamicsmentioning

confidence: 99%

“…The cluster algorithm is usually implemented in two steps. In the first step, one performs a "freeze-delete" operation on the bonds using a fixed set of rules [12,13], which results in the formation of independent clusters. The second step consists in flipping these clusters.…”

Section: Cluster Dynamicsmentioning

confidence: 99%

“…The freeze-delete operations are exactly as in Ref. [13] and are effected without considering the energy associated with the staggered field. In the second step, we calculate the staggered-field energy of every cluster and then flip it using heat-bath rules.…”

Section: Cluster Dynamicsmentioning

confidence: 99%

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Triangular Ising antiferromagnet in a staggered field

2000

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We study the equilibrium properties of the nearestneighbor Ising antiferromagnet on a triangular lattice in the presence of a staggered field conjugate to one of the degenerate ground states. Using a mapping of the ground states of the model without the staggered field to dimer coverings on the dual lattice, we classify the ground states into sectors specified by the number of "strings". We show that the effect of the staggered field is to generate long-range interactions between strings. In the limiting case of the antiferromagnetic coupling constant J becoming infinitely large, we prove the existence of a phase transition in this system and obtain a finite lower bound for the transition temperature. For finite J, we study the equilibrium properties of the system using Monte Carlo simulations with three different dynamics. We find that in all the three cases, equilibration times for low field values increase rapidly with system size at low temperatures. Due to this difficulty in equilibrating sufficiently large systems at low temperatures, our finite-size scaling analysis of the numerical results does not permit a definite conclusion about the existence of a phase transition for finite values of J. A surprising feature in the system is the fact that unlike usual glassy systems, a zero-temperature quench almost always leads to the ground state, while a slow cooling does not.

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Section: Cluster Dynamicsmentioning

confidence: 99%

Section: Cluster Dynamicsmentioning

confidence: 99%

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Triangular Ising antiferromagnet in a staggered field

2000

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“…where w α satisfy eq.(16). Due to (16) and (18)these probabilities are normalized for any spin configuration…”

Section: H({smentioning

confidence: 99%

“…[12,13] Recently Kandel, Ben-Av and Domany have introduced a new type of MC cluster algorithm for the particular case of the fully frustrated Ising model [14] which is able to reduce the critical slowing down. Attempts to use their algorithm to other frustrated models has been satisfactory in few cases [15,16] and discouraging in others [17,18]. A different approach based on the definition of quasi-frozen clusters in spin glasses looks very promising, but the implementation of a related cluster dynamics has not been yet explored [19].…”

Section: Introductionmentioning

confidence: 99%

Percolation and cluster Monte Carlo dynamics for spin models

et al. 1996

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A general scheme for devising efficient cluster dynamics proposed in a previous paper ͓Phys. Rev. Lett. 72, 1541 ͑1994͔͒ is extensively discussed. In particular, the strong connection among equilibrium properties of clusters and dynamic properties as the correlation time for magnetization is emphasized. The general scheme is applied to a number of frustrated spin models and the results discussed. ͓S1063-651X͑96͒08406-1͔

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A worm algorithm for the fully-packed loop model

2009

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We present a Markov-chain Monte Carlo algorithm of worm type that correctly simulates the fully-packed loop model on the honeycomb lattice, and we prove that it is ergodic and has uniform stationary distribution. The fully-packed loop model on the honeycomb lattice is equivalent to the zero-temperature triangular-lattice antiferromagnetic Ising model, which is fully frustrated and notoriously difficult to simulate. We test this worm algorithm numerically and estimate the dynamic exponent z = 0.515(8). We also measure several static quantities of interest, including loop-length and face-size moments. It appears numerically that the face-size moments are governed by the magnetic dimension for percolation.Comment: 31 pages, 10 figures. Several new figures added, and some minor typos corrected. Uses the following latex packages: algorithm.sty, algorithmic.sty, elsart-num.bst, elsart1p.cls, elsart.cl

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Cluster Monte Carlo dynamics for the antiferromagnetic Ising model on a triangular lattice

Cited by 15 publications

References 24 publications

Triangular Ising antiferromagnet in a staggered field

Triangular Ising antiferromagnet in a staggered field

Percolation and cluster Monte Carlo dynamics for spin models

A worm algorithm for the fully-packed loop model

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