Unusual universality of branching interfaces in random media

Kardar, Mehran; Stella, Attilio L.; Sartoni, G.; Derrida, Bernard

doi:10.1103/physreve.52.r1269

Cited by 44 publications

(95 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is based on numerical results on the random Ising model [22][23][24], the Ashkin-Teller model and the four-state Potts model [7] † (all of which exhibit continuous transitions in the absence of randomness), and the 8-state Potts model (which is first-order in its pure version.) It is backed up by the interface arguments of Kardar et al [8], which suggest that the Widom exponent for the random q-state Potts model is independent of q for sufficiently large q. (A similar lack of dependence on q has been argued for in the case of random Potts spin chains [26]; however, their critical behaviour is rather different in nature from that of the present case.…”

supporting

confidence: 70%

“…Monte Carlo work of Chen et al [6] on the q = 8 state Potts model and of Domany and Wiseman [7] on the Ashkin-Teller and four-state Potts models supports this conclusion, and goes further: the continuous transition found by these workers exhibits critical exponents which are consistent with those of the pure Ising model, namely γ /ν ≈ 1.75, β/ν ≈ 0.125 and α ≈ 0. An argument explaining these findings has been put forward by Kardar et al [8]. They study the properties of an J Cardy interface in the q-state random-bond Potts model at low temperatures.…”

mentioning

confidence: 97%

See 1 more Smart Citation

The homology groups of the variety of complete pairs $ X_{13}$ of zero-dimensional subschemes of lengths 1 and 3 of projective space

Тимофеева¹

2000

Sb. Math.

View full text Add to dashboard Cite

We analyse the effect of quenched uncorrelated randomness coupling to the local energy density of a model consisting of N coupled two-dimensional Ising models. For N > 2 the pure model exhibits a fluctuation-driven first-order transition, characterized by runaway renormalization-group behaviour. We show that the addition of weak randomness acts to stabilize these flows, in such a way that the trajectories ultimately flow back towards the pure decoupled Ising fixed point, with the usual critical exponents α = 0, ν = 1, apart from logarithmic corrections. We also show by examples that, in higher dimensions, such transitions may either become continuous or remain first-order in the presence of randomness.

show abstract

supporting

confidence: 70%

mentioning

confidence: 97%

The homology groups of the variety of complete pairs $ X_{13}$ of zero-dimensional subschemes of lengths 1 and 3 of projective space

Тимофеева¹

2000

Sb. Math.

View full text Add to dashboard Cite

show abstract

“…It has been conjectured [16] that critical random Potts models are equivalent to Ising models. Kardar et al [17] suggested a possible mechanism for this effect. Their position space renormalization group approximation suggests that the probability of loop formation in the fractal interface of the clean system vanishes marginally at a transition dominated by random bonds.…”

mentioning

confidence: 99%

Domain Walls and Phase Transitions in the Frustrated Two-DimensionalXYModel

Denniston

Tang²

1997

Phys. Rev. Lett.

View full text Add to dashboard Cite

We compare the critical properties of the two-dimensional (2D) XY model in a transverse magnetic field with filling factors f = 1/3 and 2/5. To obtain a comparison with recent experiments, we investigate the effect of weak quenched bond disorder for f = 2/5. A finite-size scaling analysis of extensive Monte Carlo simulations strongly suggests that the critical exponents of the phase transition for f = 1/3 and for f = 2/5 with disorder, fall into the 2D Ising model universality class. Studying the possible domain walls in the system provides some explanations for our results. 64.70.Rh, 05.70.Fh, 64.60.Fr, 74.50.+r The frustrated XY model provides a convenient framework to study a variety of fascinating phenomena displayed by numerous physical systems. One experimental realization of this model is in two-dimensional arrays of Josephson junctions and superconducting wire networks [1][2][3]. A perpendicular magnetic field induces a finite density of circulating supercurrents, or vortices, within the array. The interplay of two length scales -the mean separation of vortices and the period of the underlying physical array -gives rise to a wide variety of interesting physical phenomena. Many of these effects show up as variations in the properties of the finite-temperature superconducting phase transitions at different fields. Recent and ongoing experiments have measured the critical exponents in superconducting arrays [3], opening the opportunity to do careful comparison of theory and experiment. In this Letter we examine the critical properties of the 2D XY model for two different values of the magnetic field in the densely frustrated regime (f ≫ 0) and in the presence of disorder.The Hamiltonian of the frustrated XY model iswhere θ j is the phase on site j of a square L × L lattice and A ij = (2π/φ 0 ) j i A · dl is the integral of the vector potential from site i to site j with φ 0 being the flux quantum. The directed sum of the A ij around an elementary plaquette A ij = 2πf where f , measured in the units of φ 0 , is the magnetic flux penetrating each plaquette due to the uniformly applied field. We focus here on the cases f = p/q with p/q = 1/3 and 2/5.A unit cell of the ground state fluxoid pattern for these f is shown in Figure 1(a) [4]. The pattern consists of diagonal stripes composed of a single line of vortices for f = 1 3 and a double line of vortices for f = 2 5 . (A vortex is a plaquette with unit fluxoid occupation, ie. the phase gains 2π when going around the plaquette.) The stripes shown in Figure 1(a) can sit on q sub-lattices, which we associate with members of the Z q group. They can also go along either diagonal, and we associate these two options with members of the Z 2 group. A common speculation for commensurate-incommensurate transitions and the frustrated XY model is that the transition should be in the universality class of the q-state (or 2q-state) Pott's model. We find that this is not the case because domain walls between the different states vary considerably in both energetic and ent...

show abstract

“…Their results are in excellent agreement (up to q = 4) with the theoretical predictions, in the vicinity of q = 2, originally of Ludwig [19] and improved by Dotsenko et al [16]. Thus, the study of Cardy and Jacobsen [13] has resolved and critically discussed the controversy related to the early simplifying prediction from the numerical simulations on the q = 8 RBPM, that the emerging second-order phase transitions may exhibit critical exponents consistent with those of the pure Ising (q = 2) model [11,12].…”

Section: Introductionmentioning

confidence: 82%

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

View full text Add to dashboard Cite

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.

show abstract

Unusual universality of branching interfaces in random media

Cited by 44 publications

References 17 publications

The homology groups of the variety of complete pairs $ X_{13}$ of zero-dimensional subschemes of lengths 1 and 3 of projective space

The homology groups of the variety of complete pairs $ X_{13}$ of zero-dimensional subschemes of lengths 1 and 3 of projective space

Domain Walls and Phase Transitions in the Frustrated Two-DimensionalXYModel

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

Contact Info

Product

Resources

About