Study of a square-lattice Ising superantiferromagnet using the Wang–Landau algorithm and partition function zeros

Lee, Jae‐Hwan; Song, Hak Jun; Kim, Jin Min; Kim, Seung‐Yeon

doi:10.1088/1742-5468/2010/03/p03020

Cited by 15 publications

(6 citation statements)

References 42 publications

(69 reference statements)

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“…In summary, while a signature of a first-order transition is observed at κ = 0.48, a pronounced finite-size dependence of various observables prevents a clear characterization of the range κ † < κ < 1/2. We nevertheless differentiated sizable pre-asymptotic corrections that had previously been (incorrectly) associated with a continuous transition [18,35,49]. Particular caution should thus be applied to future studies of this regime.…”

Section: For An Ashkin-teller (At)-type Phase Transitionmentioning

confidence: 76%

Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices

Hu,

Charbonneau

2021

Preprint

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Ising models with frustrated next-nearest-neighbor interactions present a rich morphology of modulated phases. These phases, however, assemble and relax slowly, which hinders their computational study. In two dimensions, strong fluctuations further hamper determining their equilibrium phase behavior from theoretical approximations. The exact numerical transfer matrix (TM) method, which bypasses these difficulties, can serve as a benchmark method once its own numerical challenges are surmounted. Building on our recent study [Hu and Charbonneau, Phys. Rev. B 103, 094441 (2021)], in which we evaluated the two-dimensional axial next-nearest-neighbor Ising (ANNNI) model with transfer matrices, we here extend the effective usage of the TM method into the Ising models with biaxial, diagonal, and third-nearest-neighbor frustrations (BNNNI, DNNI, and 3NNI models). Thanks to the high-accuracy numerics provided by the TM results, various physical ambiguities about these reference models are resolved and an overview of modulated phase formation is obtained.

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Section: For An Ashkin-teller (At)-type Phase Transitionmentioning

confidence: 76%

Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices

Hu,

Charbonneau

2021

Preprint

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“…As the system size increases, z 0 are expected to approach the critical point on the positive real axis. The imaginary parts of z 0 show a finite-size scaling [44][45][46][47] Im…”

Section: Numerical Resultsmentioning

confidence: 99%

Single transition of discrete Laplacian roughening model on a square lattice

Lee¹,

Kim²

2022

J. Stat. Mech.

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We study the discrete Laplacian roughening surface model on a square lattice. The specific heat is calculated by the density of states, which is obtained by the Wang–Landau Monte Carlo simulation method. We find a single second-order phase transition which is not the Kosterlitz–Thouless transition, and obtain the critical exponents ν = 0.711(13) and α = 0.601(28). The finite-size scaling analysis for the first zeros of the partition function confirms the exponents independently.

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“…Less is known about the antiferromagnetic Ising model on a square lattice when further neighbor interactions are included. Various issues regarding the nature of the phase transitions are still being discussed when next-nearest-neighbor interactions are included in either the presence of [50,51] or the absence of [52,53] an applied magnetic field. For interactions out to third-nearest neighbors, only the most basic features of the phase diagram are known even in the absence of an applied magnetic field [54].…”

Section: Theorymentioning

confidence: 99%

Charge-regulation phase transition on surface lattices of titratable sites adjacent to electrolyte solutions: An analog of the Ising antiferromagnet in a magnetic field

Shore

Thurston

2015

Phys. Rev. E

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We report a charge-patterning phase transition on two-dimensional square lattices of titratable sites, here regarded as protonation sites, placed in a low-dielectric medium just below the planar interface between this medium and a salt solution. We calculate the work-of-charging matrix of the lattice with use of a linear Debye-Hückel model, as input to a grand-canonical partition function for the distribution of occupancy patterns. For a large range of parameter values, this model exhibits an approximate inverse cubic power-law decrease of the voltage produced by an individual charge, as a function of its in-lattice separation from neighboring titratable sites. Thus, the charge coupling voltage biases the local probabilities of proton binding as a function of the occupancy of sites for many neighbors beyond the nearest ones. We find that even in the presence of these longer-range interactions, the site couplings give rise to a phase transition in which the site occupancies exhibit an alternating, checkerboard pattern that is an analog of antiferromagnetic ordering. The overall strength W of this canonical charge coupling voltage, per unit charge, is a function of the Debye length, the charge depth, the Bjerrum length, and the dielectric coefficients of the medium and the solvent. The alternating occupancy transition occurs above a curve of thermodynamic critical points in the (pH-pK,W) plane, the curve representing a charge-regulation analog of variation of the Néel temperature of an Ising antiferromagnet as a function of an applied, uniform magnetic field. The analog of a uniform magnetic field in the antiferromagnet problem is a combination of pH-pK and W, and 1/W is the analog of the temperature in the antiferromagnet problem. We use Monte Carlo simulations to study the occupancy patterns of the titratable sites, including interactions out to the 37th nearest-neighbor category (a distance of 74 lattice constants), first validating simulations through comparison with exact and approximate results for the nearest-neighbor case. We then use the simulations to map the charge-patterning phase boundary in the (pH-pK,W) plane. The physical parameters that determine W provide a framework for identifying and designing real surfaces that could exhibit charge-patterning phase transitions.

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Study of a square-lattice Ising superantiferromagnet using the Wang–Landau algorithm and partition function zeros

Abstract: We study the square-lattice Ising model with nearest-neighbor (J 1 )

Cited by 15 publications

References 42 publications

Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices

Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices

Single transition of discrete Laplacian roughening model on a square lattice

Charge-regulation phase transition on surface lattices of titratable sites adjacent to electrolyte solutions: An analog of the Ising antiferromagnet in a magnetic field

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