Correlations in inhomogeneous Ising models

Wolff, W. F.; Zittartz, J.

doi:10.1007/bf01313801

Cited by 29 publications

(14 citation statements)

References 27 publications

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“…The other at a lower temperature T 0 (q), in the same universality class of the fully frustrated Ising model. In the bidimensional case T 0 (q) = 0 [25][26][27].…”

Section: The "Q-bond Frustrated Percolation" Modelmentioning

confidence: 99%

“…To gain more insight into the mechanisms which lead to the appearing of anomalies in the dynamical behavior, in this paper we study the fully frustrated Ising model [25][26][27] on a bidimensional square lattice, using the conventional spin flip techniques. In this model ferromagnetic and antiferromagnetic interactions are distributed in a regular way on the lattice (see Fig.…”

Section: Introductionmentioning

confidence: 99%

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Nonexponential relaxation in fully frustrated models

1997

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We study the dynamical properties of the fully frustrated Ising model. Due to the absence of disorder the model, contrary to spin glass, does not exhibit any Griffiths phase, which has been associated to non-exponential relaxation dynamics. Nevertheless we find numerically that the model exhibits a stretched exponential behavior below a temperature Tp corresponding to the percolation transition of the Kasteleyn-Fortuin clusters. We have also found that the critical behavior of this clusters for a fully frustrated q-state spin model at the percolation threshold is strongly affected by frustration. In fact while in absence of frustration the q = 1 limit gives random percolation, in presence of frustration the critical behavior is in the same universality class of the ferromagnetic q = 1/2-state Potts model.

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“…The other at a lower temperature T 0 (q), in the same universality class of the fully frustrated Ising model. In the bidimensional case T 0 (q) = 0 [25][26][27].…”

Section: The "Q-bond Frustrated Percolation" Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonexponential relaxation in fully frustrated models

1997

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“…Section 4 is the central part of this article; it is devoted to our study of the above mentioned two-spin correlation. As in numerous previous investigations of correlations in Ising models on various two-dimensional lattices [7,8,9,10,11,12,13,14,15], the correlation function considered here is found to be represented rigorously by a Toeplitz determinant. By evaluating this determinant [16,17] we obtain analytic expressions for χ(m, n) in the limit of large distances between the spins, |n − m| ≫ 1, in various regions and on various special lines of the phase diagram.…”

Section: Introductionmentioning

confidence: 67%

Correlations in the Ising antiferromagnet on the anisotropic kagome lattice

Apel¹,

Everts²

2011

J. Stat. Mech.

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Abstract. We study the correlation function of middle spins, i. e. of spins on intermediate sites between two adjacent parallel lattice axes, of the spatially anisotropic Ising antiferromagnet on the kagome lattice. It is given rigorously by a Toeplitz determinant. The large-distance behaviour of this correlation function is obtained by analytic methods. For shorter distances we evaluate the Toeplitz determinant numerically. The correlation function is found to vanish exactly on a line J d (T ) in the T − J (temperature vs. coupling constant) phase diagram. This disorder line divides the phase diagram into two regions. For J < J d (T ) the correlations display the features of an unfrustrated two-dimensional Ising magnet, whereas for J > J d (T ) the correlations between the middle spins are seen to be strongly influenced by the shortrange antiferromagnetic order that prevails among the spins of the adjacent lattice axes. While for J < J d (T ) there is a region with ferrimagnetic long-range order, the model remains disordered for J > J d (T ) down to T = 0.Submitted to: JSTAT Correlations in the Ising antiferromagnet on the anisotropic kagome lattice

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“…In function p, odd power terms of spin variables do not appear by the invariance for all the spin inversion. Further, for sufficiently large separation between i and j sites (li-jl~L), each factor in (4·2) is estimated from the exact expression of asymptotic formula 3 ) as (4·4) where the double signs + and -depend on even and odd number of antiferromagnetic bonds, respectively on the shortest path between i and j sites and each replica factor takes simultaneously the same one of double signs. Thus, the function r is estimated …”

Section: Iss'}mentioning

confidence: 99%

“…On the other hand, the pair spin correlation function at OK exhibits a long-ranged algebraic decay2), 3) and it is expected that some physical quantities show anomalous behavior near OK. In fact, we can find an external field which enhances those spin configurations induced preferably by the frustrated interaction.…”

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confidence: 99%

Response of Fully-Frustrated Ising Square Lattice to a Type of Symmetry Breaking Field

Kasai

Ohnaka

1992

Progress of Theoretical Physics

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219The fully-frustrated Ising system without the frozen spin state shows the diverging behavior with the critical index 8=3 in the response to a replica type·of field at low temperature. The replica field provides a relevant external field for a specific Villain-Stephenson universality class treated recently by Horiguchi, Tanaka and Morita.' § 1. IntroductionFor typical 2D strongly-frustrated Ising lattices, it is rigorously proved that the phase is paramagnetic ~t any finite temperature.1H ) That is, there exists no symmetry broken state and thermodynamic functions are invariant for all the spin inversion. On the other hand, the pair spin correlation function at OK exhibits a long-ranged algebraic decay2),3) and it is expected that some physical quantities show anomalous behavior near OK. In fact, we can find an external field which enhances those spin configurations induced preferably by the frustrated interaction. More concretely, we can provide a conjugate external field of frustrated spin configurations by an excellent device called real replica method. Originally, the reall-eplica method is invented by Suzuki 4 ),5) and developed by Suzuki and Miyashita 6 ) to detect the spin glass order. The essential point is that the best reference of an order in an Ising lattice, if it exists in some sense, is the identical lattice. We can regard the replicated lattice as the conjugate field of order. The response of a 2D frustrated lattice to the replica field is investigated by simulation. The data show a type of response diverging behavioe) with the exponent 0'=3. Scaling analysis supports the result. We try to interpret this behavior as an indication of ordered state even for the 2D fully-frustrated lattices.In § 2, the replica method is reformulated. In § 3, for the fully-frustrated square lattice, the simulation is performed to obtain the response to the replica field, i. e., the conjugate magnetization and susceptibility. In § 4, a scaling interpretation for the response is presented, and in § 5 concluding remarks are made. § 2. Replica field We prepare two layers or replicas of Ising Lx L square lattice with an appropriate fully-frustrated arrangement of exchange integrals J ij between i-th and j-th sites (each of them takes + J or -n. We assign additional exchange integrals Jz between all the pair of corresponding spins on two replicas. Designate the spin value of i-th site on the first replica as S/1) and that on the second one as SpY. Then, the Hamiltonian H of this replicated lattice can be written as

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Correlations in inhomogeneous Ising models

Cited by 29 publications

References 27 publications

Nonexponential relaxation in fully frustrated models

Nonexponential relaxation in fully frustrated models

Correlations in the Ising antiferromagnet on the anisotropic kagome lattice

Response of Fully-Frustrated Ising Square Lattice to a Type of Symmetry Breaking Field

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