Criticality in the randomness-induced second-order phase transition of the triangular Ising antiferromagnet with nearest- and next-nearest-neighbor interactions

Abstract

Using a Wang-Landau entropic sampling scheme, we investigate the effects of quenched bond randomness on a particular case of a triangular Ising model with nearest- ($J_{nn}$) and next-nearest-neighbor ($J_{nnn}$) antiferromagnetic interactions. We consider the case $R=J_{nnn}/J_{nn}=1$, for which the pure model is known to have a columnar ground state where rows of nearest-neighbor spins up and down alternate and undergoes a weak first-order phase transition from the ordered to the paramagnetic state. With the introduction of quenched bond randomness we observe the effects signaling the expected conversion of the first-order phase transition to a second-order phase transition and using the Lee-Kosterlitz method, we quantitatively verify this conversion. The emerging, under random bonds, continuous transition shows a strongly saturating specific heat behavior, corresponding to a negative exponent $\alpha$, and belongs to a new distinctive universality class with $\nu =1.135(11)$, $\gamma /\nu =1.744(9)$, and $\beta /\nu =0.124(8)$. Thus, our results for the critical exponents support an extensive but weak universality and the emerged continuous transition has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of two-dimensional (2d) systems without and with quenched disorder.

17 pages, 6 figures, accepted for publication in Physica A

References in corpus (31)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
• Fast Algorithm to Calculate Density of States
• Critical Behavior of Random Bond Potts Models
• Lack of Self-Averaging in Critical Disordered Systems
• Critical Behaviour of Random Bond Potts Models: A Transfer Matrix Study
• Self-Averaging, Distribution of Pseudo-Critical Temperatures and Finite Size Scaling in Critical Disordered Systems
• Renormalisation group calculation of correlation functions for the 2D random bond Ising and Potts models
• Finite-Size Scaling Study of the Surface and Bulk Critical Behavior in the Random-Bond 8-state Potts Model
• Ising exponents in the two-dimensional site-diluted Ising model
• Strong Violation of Critical Phenomena Universality: Wang-Landau Study of the 2d Blume-Capel Model under Bond Randomness
• Quenched Randomness at First-Order Transitions
• Evidence for softening of first-order transition in 3D by quenched disorder
• Estimation of critical behavior from the density of states in Classical Statistical Models
• Weak Randomness for large q-State Potts models in Two Dimensions
• Effect of Random Impurities on Fluctuation-Driven First Order Transitions
• Effect of Dilution on First Order Transitions: The Three Dimensional Three States Potts Model
• Critical behaviour of the 2d spin diluted Ising model via the equilibrium ensemble approach
• Entropic sampling via Wang-Landau random walks in dominant energy subspaces
• First-order transition features of the 3D bimodal random-field Ising model
• Specific heat of two-dimensional diluted magnets
• Crossing the coexistence line at constant magnetization
• The Unusual Universality of Branching Interfaces in Random Media
• First order transition in a three dimensional disordered system
• On weak vs. strong universality in the two-dimensional random-bond Ising ferromagnet
• The Blume-Emery-Griffiths Spin Glass and Inverted Tricritical Points
• Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
• Random Bond Potts Model: the Test of the Replica Symmetry Breaking
• Weak universality in the two dimensional randomly disordered three-state Potts ferromagnet
• First-order transition features of the triangular Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions
• A Study of Cross-Over Effects For The 2D Random Bond Potts Model

Cited by in corpus (2)

• On the non-convergence of the Wang-Landau algorithms with multiple random walkers
• Intrinsic convergence properties of entropic sampling algorithms