Tricritical and Critical End-Point Phenomena under Random Bonds

Falicov, Alexis; Berker, A. Nihat

doi:10.1103/physrevlett.76.4380

Cited by 86 publications

(92 citation statements)

References 17 publications

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“…The numerical evidence illustrated in figures 4 and 5 clearly show that the present model is out of the realm of a double logarithmic behavior predicted theoretically and numerically verified for the case of the marginal 2d RBIM [21,42,43,44,45,46,47,48,49,50]. Our conclusion, is in general agreement with the predictions of a distinctive universality class for the emerging second-order transitions [10,59], and the value ν = 1.135(11) of the correlation length's exponent is in agreement with the inequality ν ≥ 2/d for disordered systems of Chayes et al [52].…”

Section: Discussionsupporting

confidence: 88%

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

Fytas

Malakis

2009

Physica A: Statistical Mechanics and its Applications

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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 α, and belongs to a new distinctive universality class with ν = 1.135(11), γ/ν = 1.744(9), and β/ν = 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.

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Section: Discussionsupporting

confidence: 88%

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

Fytas

Malakis

2009

Physica A: Statistical Mechanics and its Applications

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“…Is it possible that stronger disorder leads to different behavior, dominated by zero temperature fixed points? This scenario is precisely what is observed in a recent position space RG of a three state random bond model [18]. Of course, another possibility is that our approximate interface model does not fully capture the physics of the system.…”

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confidence: 71%

Unusual universality of branching interfaces in random media

et al. 1995

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We study the criticality of a Potts interface by introducing a froth model which, unlike its SOS Ising counterpart, incorporates bubbles of different phases. The interface is fractal at the phase transition of a pure system. However, a position space approximation suggests that the probability of loop formation vanishes marginally at a transition dominated by strong random bond disorder. This implies a linear critical interface, and provides a mechanism for the conjectured equivalence of critical random Potts and Ising models.

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“…The TCP coordinates can be shifted and a segment of the formerly known first-order transition line can be observed as continuous transitions [5]. In the vicinity of the TCP polarization, anisotropy decreases because of the freeenergy surface flattening [6], which confirms the influence of disorder factors in mixed crystals.…”

mentioning

confidence: 86%

Ferroelectricity in (Pb_ySn_1−y)₂P₂S₆ mixed crystals and random field BEG model

Rushchanskii

Bilanych

Molnar

et al. 2015

Physica Status Solidi (b)

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In Sn2P2S6 ferroelectric under compression, the second‐order phase transition line is observed down to the tricritical point as the transition temperature decreases to 250 K. A tricriticality at a similar temperature is also revealed in the mixed crystals on S→Se substitution. For the mixed crystals with Sn→Pb substitution, ultrasound, hypersound, and low‐frequency dielectric studies also show heterophase features appearing on decrease of the ferroelectric transition temperature below a so‐called “waterline temperature” near 250 K. Such behavior agrees with the Blume–Emery–Griffiths (BEG) model appropriate for the ferroelectric system under investigation with a three‐well local potential for the order parameter fluctuations. The BEG model modified by the random‐field phase diagram in the vicinity of the tricritical point qualitatively explains the influence of the cationic substitution on the (PbySn1−y)2P2S6 ferroelectric properties.

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Tricritical and Critical End-Point Phenomena under Random Bonds

Cited by 86 publications

References 17 publications

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

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

Unusual universality of branching interfaces in random media

Ferroelectricity in (Pb_ySn_1−y)₂P₂S₆ mixed crystals and random field BEG model

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Tricritical and Critical End-Point Phenomena under Random Bonds

Cited by 86 publications

References 17 publications

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

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

Unusual universality of branching interfaces in random media

Ferroelectricity in (PbySn1−y)2P2S6 mixed crystals and random field BEG model

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Ferroelectricity in (Pb_ySn_1−y)₂P₂S₆ mixed crystals and random field BEG model