Thermodynamics of the classical spin-ice model with nearest neighbour interactions using the Wang-Landau algorithm

Ferreyra, María Victoria; Giordano, Gaston Luciano; Borzi, R. A.; Betouras, Joseph J.; Grigera, S. A.

doi:10.1140/epjb/e2016-60781-7

Cited by 15 publications

(19 citation statements)

References 35 publications

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“…[21], which remains unclear. Finally, in 2016, Ferreyra et al [26], used Wang-Landau (WL) simulations in nearest-neighbor spin-ice to give an estimate of the residual density of states, which is also in accordance with Nagle's estimate.…”

Section: Numerical Workmentioning

confidence: 77%

Boundary conditions and the residual entropy of ice systems

Ferreyra

Grigera

2018

Phys. Rev. E

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In this work we address the classical statistical mechanical problem of calculating the residual entropy of ice models. The numerical work found in the literature is usually based on extrapolating to infinite-size results obtained for finite-size systems with periodic boundary conditions. In this work we investigate how boundary conditions affect the calculation of the residual entropy for square, cubic, and hexagonal lattices using periodic, antiperiodic, and open boundary conditions. We show that periodic boundary conditions lead to noticeable oscillations in the entropy as a function of lattice size, and we calculate in open finite systems the contribution to the entropy from the open boundary. For our calculations we introduce a variation on multicanonical simulation methods that directly calculate the number of states in the ground state without the need of a Hamiltonian.

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Section: Numerical Workmentioning

confidence: 77%

Boundary conditions and the residual entropy of ice systems

Ferreyra

Grigera

2018

Phys. Rev. E

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“…A parallel WL method based on the replica-exchange framework for Monte Carlo simulations was also proposed [13]. Recently, Ferreyra et al [14] reported the calculation of g(E) for the Ising model on the pyrochlore lattice using the WL method.…”

Section: +mentioning

confidence: 99%

Entropy of diluted antiferromagnetic Ising models on frustrated lattices using the Wang-Landau method

Shevchenko¹,

Nefedev²,

Okabe³

2017

Phys. Rev. E

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We use a Monte Carlo simulation to study the diluted antiferromagnetic Ising model on the frustrated lattices including the pyrochlore lattice to show the dilution effects. Using the WangLandau algorithm, which directly calculates the energy density of states, we accurately calculate the entropy of the system. We discuss the nonmonotonic dilution concentration dependence of residual entropy for the antiferromagnetic Ising model on the pyrochlore lattice, and compare it to the generalized Pauling approximation proposed by Ke et al. [Phys. Rev. Lett. 99, 137203 (2007)]. We also investigate other frustrated systems, the antiferromagnetic Ising model on the triangular lattice and the kagome lattice, demonstrating the difference in the dilution effects between the system on the pyrochlore lattice and that on other frustrated lattices. This paper is accepted for publication in Phys. Rev. E

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“…Unlike spin ice models, our model "water oxygens" possess interacting dipoles, whereas the only interaction between hydrogens ("spins") comes from the topological IR constraints. These analogies and differences underpin those that will appear in the equilibrium phase diagram, reminiscent of but not identical to the three-dimensional (3D) Kasteleyn transition (31) of spin ice in a field (32,33), as well as to the out-of-equilibrium, proton ordering behavior. The kinetic process by which the dopant triggers proton ordering is an avalanche of proton hoppings, which, breaking up closed rings, generates strings of collinear hydrogen bonds, all pointing in the same direction along a winding line, thus upsetting the ring landscape of the disordered phase.…”

Section: Significancementioning

confidence: 87%

“…1 D, Inset. Pauling's entropy is known to be only a lower bound (33). Our HREM calculations capture the addi-tional proton correlations along the closed rings, which cause entropy to rise higher for smaller sizes (40).…”

Section: Modelmentioning

confidence: 98%

Proton strings and rings in atypical nucleation of ferroelectricity in ice

Lasave

Koval

Laio

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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Ordinary ice has a proton-disordered phase which is kinetically metastable, unable to reach, spontaneously, the ferroelectric (FE) ground state at low temperature where a residual Pauling entropy persists. Upon light doping with KOH at low temperature, the transition to FE ice takes place, but its microscopic mechanism still needs clarification. We introduce a lattice model based on dipolar interactions plus a competing, frustrating term that enforces the ice rule (IR). In the absence of IR-breaking defects, standard Monte Carlo (MC) simulation leaves this ice model stuck in a state of disordered proton ring configurations with the correct Pauling entropy. A replica exchange accelerated MC sampling strategy succeeds, without open path moves, interfaces, or off-lattice configurations, in equilibrating this defect-free ice, reaching its low-temperature FE order through a well-defined first-order phase transition. When proton vacancies mimicking the KOH impurities are planted into the IR-conserving lattice, they enable standard MC simulation to work, revealing the kinetics of evolution of ice from proton disorder to partial FE order below the transition temperature. Replacing ordinary nucleation, each impurity opens up a proton ring generating a linear string, an actual FE hydrogen bond wire that expands with time. Reminiscent of those described for spin ice, these impurity-induced strings are proposed to exist in doped water ice too, where IRs are even stronger. The emerging mechanism yields a dependence of the long-time FE order fraction upon dopant concentration, and upon quenching temperature, that compares favorably with that known in real-life KOH doped ice.

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Thermodynamics of the classical spin-ice model with nearest neighbour interactions using the Wang-Landau algorithm

Cited by 15 publications

References 35 publications

Boundary conditions and the residual entropy of ice systems

Boundary conditions and the residual entropy of ice systems

Entropy of diluted antiferromagnetic Ising models on frustrated lattices using the Wang-Landau method

Proton strings and rings in atypical nucleation of ferroelectricity in ice

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