Wang–Landau study of the random bond square Ising model with nearest- and next-nearest-neighbor interactions

Nikolaos G. Fytas, A. Malakis, I. Georgiou

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Abstract

We report results from a Wang–Landau study of the random bond square Ising model with nearest-neighbor (Jnn) and next-nearest-neighbor (Jnnn) antiferromagnetic interactions. We consider the case R = Jnn/Jnnn = 1 for which the competitive nature of interactions produces a sublattice ordering known as superantiferromagnetism and the pure system undergoes a second-order transition with a positive specific heat exponent α. For a particular disorder strength we study the effects of bond randomness and we find that, while the critical exponents of the correlation length ν, magnetization β, and magnetic susceptibility γ increase as compared to the pure model, the ratios β/ν and γ/ν remain unchanged. Thus, the disordered system obeys weak universality and hyperscaling similarly to other two-dimensional disordered systems. However, the specific heat exhibits an unusually strong saturating behavior which distinguishes the present case of competing interactions from other two-dimensional random bond systems studied previously.
Original languageEnglish
Article numberL07001
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2008
DOIs
Publication statusPublished - 24 Jul 2008

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Ising model
Ising Model
Nearest Neighbor
Disordered Systems
Specific Heat
Interaction
specific heat
exponents
Magnetic Susceptibility
interactions
Two-dimensional Systems
Correlation Length
Magnetization
Randomness
Critical Exponents
sublattices
Universality
Disorder
Exponent
disorders

Bibliographical note

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Cite this

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title = "Wang–Landau study of the random bond square Ising model with nearest- and next-nearest-neighbor interactions",
abstract = "We report results from a Wang–Landau study of the random bond square Ising model with nearest-neighbor (Jnn) and next-nearest-neighbor (Jnnn) antiferromagnetic interactions. We consider the case R = Jnn/Jnnn = 1 for which the competitive nature of interactions produces a sublattice ordering known as superantiferromagnetism and the pure system undergoes a second-order transition with a positive specific heat exponent α. For a particular disorder strength we study the effects of bond randomness and we find that, while the critical exponents of the correlation length ν, magnetization β, and magnetic susceptibility γ increase as compared to the pure model, the ratios β/ν and γ/ν remain unchanged. Thus, the disordered system obeys weak universality and hyperscaling similarly to other two-dimensional disordered systems. However, the specific heat exhibits an unusually strong saturating behavior which distinguishes the present case of competing interactions from other two-dimensional random bond systems studied previously.",
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AU - Fytas, Nikolaos G.

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AU - Georgiou, I.

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N2 - We report results from a Wang–Landau study of the random bond square Ising model with nearest-neighbor (Jnn) and next-nearest-neighbor (Jnnn) antiferromagnetic interactions. We consider the case R = Jnn/Jnnn = 1 for which the competitive nature of interactions produces a sublattice ordering known as superantiferromagnetism and the pure system undergoes a second-order transition with a positive specific heat exponent α. For a particular disorder strength we study the effects of bond randomness and we find that, while the critical exponents of the correlation length ν, magnetization β, and magnetic susceptibility γ increase as compared to the pure model, the ratios β/ν and γ/ν remain unchanged. Thus, the disordered system obeys weak universality and hyperscaling similarly to other two-dimensional disordered systems. However, the specific heat exhibits an unusually strong saturating behavior which distinguishes the present case of competing interactions from other two-dimensional random bond systems studied previously.

AB - We report results from a Wang–Landau study of the random bond square Ising model with nearest-neighbor (Jnn) and next-nearest-neighbor (Jnnn) antiferromagnetic interactions. We consider the case R = Jnn/Jnnn = 1 for which the competitive nature of interactions produces a sublattice ordering known as superantiferromagnetism and the pure system undergoes a second-order transition with a positive specific heat exponent α. For a particular disorder strength we study the effects of bond randomness and we find that, while the critical exponents of the correlation length ν, magnetization β, and magnetic susceptibility γ increase as compared to the pure model, the ratios β/ν and γ/ν remain unchanged. Thus, the disordered system obeys weak universality and hyperscaling similarly to other two-dimensional disordered systems. However, the specific heat exhibits an unusually strong saturating behavior which distinguishes the present case of competing interactions from other two-dimensional random bond systems studied previously.

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