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arXiv:1702.04340 · Condensed Matter Physics

Emergent universal critical behavior of the 2D N-color Ashkin-Teller model in the presence of correlated disorder

M. Dudka, Andrei A. Fedorenko

Published Mar 1, 2017• 1 citation
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Abstract

We study the critical behavior of the 2D N-color Ashkin-Teller model in the presence of random bond disorder whose correlations decays with the distance r as a power-law r -a .We consider the case when the spins of different colors sitting at the same site are coupled by the same bond and map this problem onto the 2D system of N/2 flavors of interacting Dirac fermions in the presence of correlated disorder.Using renormalization group we show that for N = 2, a "weakly universal" scaling behavior at the continuous transition becomes universal with new critical exponents.For N > 2, the first-order phase transition is rounded by the correlated disorder and turns into a continuous one.

DOI
10.5488/cmp.20.13603

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We study the critical behavior of the 2D N-color Ashkin-Teller model in the presence of random bond disorder whose correlations decays with the distance r as a power-law r -a .We consider the case when the spins of different colors sitting at the same site are coupled by the same bond and map this problem onto the 2D system of N/2 flavors of interacting Dirac fermions in the presence of correlated disorder.Using renormalization group we show that for N = 2, a "weakly universal" scaling behavior at the continuous transition becomes universal with new critical exponents.For N > 2, the first-order phase transition is rounded by the correlated disorder and turns into a continuous one.
We study the effects of quenched disorder on the first-order phase transition in the two-dimensional three-color Ashkin-Teller model by means of large-scale Monte Carlo simulations. We demonstrate that the first-order phase transition is rounded by the disorder and turns into a continuous one. Using a careful finite-size-scaling analysis, we provide strong evidence for the emerging critical behavior of the disordered Ashkin-Teller model to be in the clean two-dimensional Ising universality class, accompanied by universal logarithmic corrections. This agrees with perturbative renormalization-group predictions by Cardy. As a byproduct, we also provide support for the strong-universality scenario for the critical behavior of the two-dimensional disordered Ising model. We discuss consequences of our results for the classification of disordered phase transitions as well as generalizations to other systems.
We investigate the two‐dimensional four‐color Ashkin‐Teller model by means of large‐scale Monte‐Carlo simulations. We demonstrate that the first‐order phase transition of the clean system is destroyed by random disorder introduced via site dilution. The critical behavior of the emerging continuous transition belongs to the clean two‐dimensional Ising universality class, apart from logarithmic corrections. These results confirm perturbative renormalization‐group predictions; they also agree with recent findings for the three‐color case, indicating that the critical behavior is universal.
Abstract The N -color Ashkin–Teller model corresponds to N Ising models coupled by four-spin interactions. We consider the two-dimensional case in presence of quenched disorder and use scale invariant scattering theory to determine all the solutions of the exact renormalization group fixed points equations. The weak disorder sector is characterized by a solution that, for any fixed N larger than 1, is a line of fixed points with Ising thermal exponents and continuously varying magnetic exponents. The number of fixed point solutions allowed by the symmetries of the model increases at strong disorder illustrating the growing dependence on the distributions of the two random couplings. The presence of some critical exponents which do not depend on the symmetry parameter N confirms this type of superuniversality as a peculiar feature of random criticality.
An intriguing result of statistical mechanics is that a first-order phase transition can be rounded by disorder coupled to energylike variables. In fact, even more intriguing is that the rounding may manifest itself as a critical point, quantum or classical. In general, it is not known, however, what universality classes, if any, such criticalities belong to. In order to shed light on this question we examine in detail the disordered three-color Ashkin-Teller model by Monte Carlo methods. Extensive analyses indicate that the critical exponents define a new universality class. We show that the rounding of the first-order transition of the pure model due to the impurities is manifested as criticality. However, the magnetization critical exponent, β, and the correlation length critical exponent, ν, are found to vary with disorder and the four-spin coupling strength, and we conclusively rule out that the model belongs to the universality class of the two-dimensional Ising model.
The N -color quantum Ashkin–Teller spin chain is a prototypical model for the study of strong-randomness phenomena at first-order and continuous quantum phase transitions. In this paper, we first review the existing strong-disorder renormalization group approaches to the random quantum Ashkin–Teller chain in the weak-coupling as well as the strong-coupling regimes. We then introduce a novel general variable transformation that unifies the treatment of the strong-coupling regime. This allows us to determine the phase diagram for all color numbers N , and the critical behavior for all . In the case of two colors, N = 2, a partially ordered product phase separates the paramagnetic and ferromagnetic phases in the strong-coupling regime. This phase is absent for all , i.e., there is a direct phase boundary between the paramagnetic and ferromagnetic phases. In agreement with the quantum version of the Aizenman–Wehr theorem, all phase transitions are continuous, even if their clean counterparts are of first order. We also discuss the various critical and multicritical points. They are all of infinite-randomness type, but depending on the coupling strength, they belong to different universality classes.
We investigate the zero-temperature quantum phase transitions of the disordered three-color quantum Ashkin-Teller spin chain by means of large-scale Monte Carlo simulations. We find that the first-order phase transitions of the clean system are rounded by the quenched disorder. For weak intercolor coupling, the resulting emergent quantum critical point between the paramagnetic phase and the magnetically ordered Baxter phase is of infinite-randomness type and belongs to the universality class of the random transverse-field Ising model, as predicted by recent strong-disorder renormalization group calculations. We also find evidence for unconventional critical behavior in the case of strong intercolor coupling, even though an unequivocal determination of the universality class is beyond our numerical capabilities. We compare our results to earlier simulations, and we discuss implications for the classification of phase transitions in the presence of disorder.