Random layered frustration models

We study the ground-state entanglement of two halves of a critical transverse Ising chain, separated by an interface defect. From the relation to a two-dimensional Ising model with a defect line we obtain an exact expression for the continuously varying effective central charge which governs the asymptotic behaviour of the entanglement entropy. The result is relevant also for other fermionic chains.

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“…Such calculations have, of course, been done also in other studies dealing with layered Ising lattices, see e.g. [33][34][35].…”

Section: Appendix Amentioning

confidence: 99%

Entanglement in fermionic chains with interface defects

Eisler

Peschel

2010

Annalen der Physik

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“…in terms of the σ x l , σ z l Pauli matrices at site l. Here the exchange couplings J l and the transverse fields h l are quenched random variables, taken independently from distributions π(J) and ρ(h), respectively. The quantum model in (1.1) is closely related to a two-dimensional classical Ising model with randomly layered couplings, which was first introduced and partially solved by McCoy and Wu [15,16] (see also [17][18][19] For δ < 0 (δ > 0) the system is in the ordered (disordered) phase and at δ = 0 there is a phase transition in the system. One surprising observation is that at the critical point some physical quantities are not self-averaging, thus the typical and the average values of those are different.…”

Section: Introductionmentioning

confidence: 99%

Comparative study of the critical behavior in one-dimensional random and aperiodic environments

Iglói¹,

Karevski²,

Rieger³

1998

Eur. Phys. J. B

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We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents ω > 0. At the critical point the random and aperiodic systems scale essentially anisotropically in a similar fashion: length (L) and time (t) scales are related as L ∼ (ln t) 1/ω . Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of ω, whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important difference between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities.

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“…7 Besides, for our model the HoeverWolff-Zittartz conjecture 17 One observes that for a G [ -0.91, -1] there are the following successive phases with decreasing temperature: the paramagnetic phase (P), an ordered phase (X), the reentrant P phase, and a ferromagnetic (F) phase. We note that the critical line of Fig.…”

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confidence: 97%

Coexistence of order and disorder and reentrance in an exactly solvable model

1987

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We show in this Letter exact results for the Ising model on the two-dimensional kagome lattice with nearest-and next-nearest-neighbor interactions J\ and J 2. In some regions of phase space, we find a nonzero critical temperature despite a finite zero-point entropy. For a narrow range of J2/J1 we find successive transitions with a reentrance at low temperature. We studied the nature of order by Monte Carlo method and found that in these regions one sublattice remains disordered below the transition and down to zero temperature except in the reentrant region. Thus disorder can coexist with order at equilibrium.PACS numbers: 05.50.+q, 75.40.MgOne of the most striking features of frustrated systems is the high degeneracy of the ground state (GS). The questions which arise are whether or not such a degeneracy survives at finite temperatures and how it affects thermodynamic behavior. In the case of Ising spins, it has been 1,2 pointed out that thermal and quenched disorder may select a finite number of particular GS, leading to a well-defined ordered phase at low temperatures. Extension of this idea to XY and Heisenberg 3 systems has been carried out. Such conclusions rely on low-temperature expansions which require that the selected GS upon which low-temperature expansions are performed should differ from the other GS by an infinite number of spin orientations in the thermodynamic limit. 4 This condition is not always fulfilled in frustrated systems such as the fully frustrated simple cubic lattice with Ising spins 4 and systems with finite zero-point entropy. The high GS degeneracy often yields unexpected effects such as partial disordering in the ordered phase in the fully frustrated simple cubic Ising lattice 5 and particular type of excitations 6 observed in Monte Carlo (MC) simulations.In this Letter, we study the Ising model on the kagome lattice shown in Fig. 1. This system with nearestneighbor interactions J\ has been exactly solved a long where K\^~J\,2/k^T and where the sum is performed over all spin configurations, the product is taken over all elementary cells, and periodic boundary conditions are imposed. Since there is no crossing bond interaction, our system in principle can be transformed into an exactly solvable free-fermion model. 8 Note that our model is somewhat similar to the brickboard Ising lattice recently studied by several authors. 9 " 11 To obtain the exact solution of our model, we decimate the central spin of each elementary cell of the lattice. In doing so, we obtain a checkerboard Ising model with multispin interactions. This resulting model is equivalent to a symmetrical sixteen-vertex model, 12-14 which satisfies the freefermion condition. 14 In this case an exact solution can time ago. In the present work, next-nearest-neighbor interactions J2 are taken into account. We have obtained the exact expression for the free energy from which exact results for the internal energy, specific heat, and entropy can be derived. The model has a finite zero-point entropy and undergoes a transition ...

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Random layered frustration models

Cited by 55 publications

References 9 publications

Entanglement in fermionic chains with interface defects

Entanglement in fermionic chains with interface defects

Comparative study of the critical behavior in one-dimensional random and aperiodic environments

Coexistence of order and disorder and reentrance in an exactly solvable model

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