Finite-size scaling of Monte Carlo simulations for the fcc Ising antiferromagnet: Effects of the low-temperature phase degeneracy

Stübel, Ronja; Janke, Wolfhard

doi:10.1103/physrevb.98.174413

Cited by 7 publications

(5 citation statements)

References 69 publications

(102 reference statements)

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“…As the system changes from the solid-like into the columnar phase, simulations show clear signs of a first order phase transition. From finite size scaling analysis, we find a non-standard relation predicted by a number of recent studies [43,44,51] where physical quantities scale with L 1 instead of the standard L 2 . Whether this scaling is due to the close-packed configuration degeneracy exponentially growing with system size or due to surface interactions in the domains phase still not clear.…”

Section: Discussionmentioning

confidence: 57%

Phase Transitions in Hardcore Lattice Gases on the Honeycomb Lattice

Thewes,

Fernandes

2020

Preprint

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We study lattice gas systems on the honeycomb lattice where particles exclude neighboring sites up to order k (k = 1 . . . 5) from being occupied by another particle. Monte Carlo simulations were used to obtain phase diagrams and characterize phase transitions as the system orders at high packing fractions. For systems with first neighbors exclusion (1NN), we confirm previous results suggesting a continuous transition in the 2D-Ising universality class. Exclusion up to second neighbors (2NN) lead the system to a two-step melting process where, first, a high density columnar phase undergoes a first order phase transition with non-standard scaling to a solid-like phase with short range ordered domains and, then, to fluid-like configurations with no sign of a second phase transition. 3NN exclusion, surprisingly, shows no phase transition to an ordered phase as density is increased, staying disordered even to packing fractions up to 0.98. The 4NN model undergoes a continuous phase transition with critical exponents close to the 3-state Potts model. The 5NN system undergoes two first order phase transitions, both with non-standard scaling. We, also, propose a conjecture concerning the possibility of more than one phase transition for systems with exclusion regions further than 5NN based on geometrical aspects of symmetries.

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Section: Discussionmentioning

confidence: 57%

Phase Transitions in Hardcore Lattice Gases on the Honeycomb Lattice

Thewes,

Fernandes

2020

Preprint

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show abstract

“…As the system changes from the solidlike into the columnar phase, simulations show clear signs of a first-order phase transition. From finite-size scaling analysis, we find a nonstandard relation predicted by a number of recent studies [43,44,51] where physical quantities scale with L 1 instead of the standard L 2 . Whether this scaling is due to the close-packed configuration degeneracy exponentially growing with system size or due to surface interactions in the domains phase still not clear.…”

Section: Discussionmentioning

confidence: 57%

Phase transitions in hard-core lattice gases on the honeycomb lattice

Thewes

Fernandes

2020

Phys. Rev. E

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We study lattice gas systems on the honeycomb lattice where particles exclude neighboring sites up to order k (k = 1,. .. , 5) from being occupied by another particle. Monte Carlo simulations were used to obtain phase diagrams and characterize phase transitions as the system orders at high packing fractions. For systems with first-neighbors exclusion (1NN), we confirm previous results suggesting a continuous transition in the two-dimensional Ising universality class. Exclusion up to second neighbors (2NN) lead the system to a two-step melting process where, first, a high-density columnar phase undergoes a first-order phase transition with nonstandard scaling to a solidlike phase with short-range ordered domains and, then, to fluidlike configurations with no sign of a second phase transition. 3NN exclusion, surprisingly, shows no phase transition to an ordered phase as density is increased, staying disordered even to packing fractions up to 0.98. The 4NN model undergoes a continuous phase transition with critical exponents close to the three-state Potts model. The 5NN system undergoes two first-order phase transitions, both with nonstandard scaling. We, also, propose a conjecture concerning the possibility of more than one phase transition for systems with exclusion regions further than 5NN based on geometrical aspects of symmetries.

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“…Many previous authors have looked at the near-neighbour only case [12,13,14,15,16,17,18] In our previous work [11], we analysed the case where α is positive, i.e. second neighbour interactions are ferromagnetic.…”

Section: Introductionmentioning

confidence: 99%

On the existence of an intermediate phase in the antiferromagnetic Ising model on an face-centered cubic lattice

Ackland¹

2023

Preprint

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We use Monte Carlo simulation to determine the stable structures in the second-neighbour Ising model on the face-centred cubic lattice. Those structures are L1 1 for strongly antiferromagnetic second neighbour interactions and L1 0 for ferromagnetic and weakly antiferromagnetic second neighbours. We find a third stable "intermediate" antiferromagnetic phase with I4 1 /amd symmetry, and calculate the paramagnetic transition temperature for each. The transition temperature depends strongly on second neighbour interactions which are not frustrated. Our results contradict a recent paper [1], which also reported two different AFM structures and a new "intermediate" phase exists in this system. Here we show that the assumed sublattice structure in [1] is inconsistent with the ground state. We determine a sublattice structure suitable for solving this problem with mean field theory.

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Finite-size scaling of Monte Carlo simulations for the fcc Ising antiferromagnet: Effects of the low-temperature phase degeneracy

Cited by 7 publications

References 69 publications

Phase Transitions in Hardcore Lattice Gases on the Honeycomb Lattice

Phase Transitions in Hardcore Lattice Gases on the Honeycomb Lattice

Phase transitions in hard-core lattice gases on the honeycomb lattice

On the existence of an intermediate phase in the antiferromagnetic Ising model on an face-centered cubic lattice

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