Scaling properties at the interface between different critical subsystems: The Ashkin-Teller model

Lajkó, Péter; Turban, L.; Iglói, Ferenc

doi:10.1103/physrevb.76.224423

Cited by 3 publications

(5 citation statements)

References 20 publications

(21 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this case the σ and τ spins play equivalent role and the interface critical behavior has been studied previously in Refs. [11,12]. According to these results, which are in agreement with a relevance-irrelevance analysis [2][3][4][5], the bulk fixed point (B) in the system is unstable for ǫ > 0.…”

Section: Discussionsupporting

confidence: 87%

“…For negative coupling, < 0, the structures of the phase diagrams are changed, both for symmetric and asymmetric defects. For symmetric defects the bulk fixed point becomes the stable one [11,12]. It is certainly understandable that the EI fixed point is unstable, since for < 0 ordered defects would bring a positive contribution to the energy.…”

Section: Discussionmentioning

confidence: 99%

“…The ladder and chain defects transform into each other through duality [12] and their strengths are related as follows: h ↔ 1/J. For two decoupled Ising models with = 0 the local magnetization exponents at the defect site, i = 0, generally are different for the σ and for the τ spins, which are denoted by x σ m and x τ m , respectively.…”

Section: Ladder and Chain Defectsmentioning

confidence: 99%

“…In contrast for enhanced defect couplings the defect usually renormalizes to an ordered interface and the local critical exponents are the same as at the extraordinary surface transition [6]- [8]. Examples for modified defect critical behavior can be found in the two-dimensional (2D) q = 3-state Potts model [9,10], in the Baxter-Wu model [11] and in the Ashkin-Teller (AT) model [12].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical study of the critical behavior of the Ashkin–Teller model at a line defect

Lajkó¹,

Iglói²

2011

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

We consider the Ashkin-Teller model on the square lattice, which is represented by two Ising models (σ and τ ) having a four-spin coupling of strength, ǫ, between them. We introduce an asymmetric defect line in the system along which the couplings in the σ Ising model are modified. In the Hamiltonian version of the model we study the scaling behavior of the critical magnetization at the defect, both for σ and for τ spins by density matrix renormalization. For ǫ > 0 we observe identical scaling for σ and τ spins, whereas for ǫ < 0 one model becomes locally ordered and the other locally disordered. This is different of the critical behavior of the uncoupled model (ǫ = 0) and is in contradiction with the results of recent field-theoretical calculations.

show abstract

Section: Discussionsupporting

confidence: 87%

Section: Discussionmentioning

confidence: 99%

Section: Ladder and Chain Defectsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical study of the critical behavior of the Ashkin–Teller model at a line defect

Lajkó¹,

Iglói²

2011

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Besides these new results, we hope that our approach will be useful to shed light on interesting problems concerning inhomogeneous AT-8V models. In particular it could be used to analyze scaling properties at interfaces between critical subsystems [28].…”

mentioning

confidence: 99%

Critical behavior of the spin correlation function in the Ashkin-Teller and Baxter models with a line defect

Naón

2009

Phys. Rev. E

View full text Add to dashboard Cite

We consider the critical spin-spin correlation function of the Ashkin-Teller and Baxter models.By using path-integral techniques in the continuum description of these models in terms of fermion fields, we show that the correlation decays with distance with the same critical exponent as the Ising model. The procedure is straightforwardly extended to take into account the presence of a line defect. Thus we find that in these altered models the critical index of the magnetic correlation on the defect coincides with the one of the defective 2D Ising or Bariev's model. or Baxter models [2]. These last two systems can be mapped onto one another through a duality transformation. They can be considered as two Ising magnets coupled by four-spin interactions. They are the first examples of non-universal critical behavior, in the sense that the critical exponents of certain operators are continuous functions of the parameter of the four-spin coupling. An anisotropic version of these models [3][4] leads to an interesting universality-nonuniversality crossover recently analyzed [5]. Apart from academic interest the AT and 8V models are useful to shed light on a variety of phenomena, in both classical and quantum physics, ranging from biological applications [6] to the theory of cuprate superconductors [7].Concerning the isotropic case, which we will consider in this work, it was conjectured that the magnetization keeps the Ising behavior, with a universal exponentThis result was later proved by Baxter through corner transfer matrices [4]. It is however surprising that there is no other direct computation of the two-spin correlation function in the literature.Much less is known exactly about the behavior of these systems in the presence of line defects [10]. For the simpler Ising lattice with an altered row (Bariev's model [11]) it has been shown that the scaling index of the magnetization varies continuously with the defect strength [11,12], whereas the critical exponent of the energy density at the defect line remains unchanged [13,14,15]. Taking this model as working bench, much insight was obtained about the origin of nonuniversal critical behavior. For instance, in Ref. [16] necessary conditions for the dependence of exponents on the coupling constants were derived.Interesting connections with integrable quantum field theories were also revealed [17].Despite these important advances the behavior of the spin-spin correlator for critical 8V-AT models with line defects remains unknown. The main goal of this paper is to help filling this gap. We shall derive a central feature of that critical behavior through a straightforward calculation performed within the continuous formulation of AT-8V models, using well established path-integral techniques. Since AT-8V models have both magnetic and electric correlations [4] (the electric correlations have continuously varying exponents [18]), we stress that in this paper we will be concerned with magnetic correlations only. We will show that 2 the magnetic exponent depends on t...

show abstract

Nonequilibrium critical dynamics of the two-dimensional Ising model quenched from a correlated initial state

2008

Self Cite

View full text Add to dashboard Cite

The universality class, even the order of the transition, of the two-dimensional Ising model depends on the range and the symmetry of the interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the critical temperature is generally the same due to self-duality. Here we consider a sudden change in the form of the interaction and study the nonequilibrium critical dynamical properties of the nearest-neighbor model. The relaxation of the magnetization and the decay of the autocorrelation function are found to display a power law behavior with characteristic exponents that depend on the universality class of the initial state.

show abstract

Scaling properties at the interface between different critical subsystems: The Ashkin-Teller model

Cited by 3 publications

References 20 publications

Numerical study of the critical behavior of the Ashkin–Teller model at a line defect

Numerical study of the critical behavior of the Ashkin–Teller model at a line defect

Critical behavior of the spin correlation function in the Ashkin-Teller and Baxter models with a line defect

Nonequilibrium critical dynamics of the two-dimensional Ising model quenched from a correlated initial state

Contact Info

Product

Resources

About