Order by Disorder, without Order, in a Two-Dimensional Spin System with O(2) Symmetry

Biskup, Marek; Chayes, L.; Kivelson, Steven A.

doi:10.1007/s00023-004-0196-2

Cited by 20 publications

(49 citation statements)

References 41 publications

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“…Besides these two norms, we will also need the "mixed" quantity 5) where ∧ denotes the minimum. This is not a distance function but, as will be explained in Lemma 4.2, it does satisfy an inequality which could be compared to the triangle inequality.…”

Section: Matrix Elements Of Gibbs-boltzmann Weightsmentioning

confidence: 99%

Quantum Spin Systems at Positive Temperature

Biskup

Chayes

Starr

2006

Commun. Math. Phys.

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Abstract:We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins S satisfy β √ S. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with S 1. The most notable examples are the quantum orbital-compass model on Z 2 and the quantum 120-degree model on Z 3 which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state.

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Section: Matrix Elements Of Gibbs-boltzmann Weightsmentioning

confidence: 99%

Quantum Spin Systems at Positive Temperature

Biskup

Chayes

Starr

2006

Commun. Math. Phys.

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“…2.2] for an example in the context of the 120-degree model) suggests that among all 2π possible relative orientations of the sublattices, the parallel and the antiparallel orientations are those entropically most favorable. And, indeed, as was proved in [3], there exist two 2-periodic Gibbs states µ 1 and µ 2 with the corresponding type of long-range order. However, the existence of Gibbs states with other relative orientations has not been ruled out.…”

Section: Order-by-disorder Transitionsmentioning

confidence: 64%

“…Unfortunately, no conclusion of this kind is currently available in the approaches based solely on chessboard estimates. This makes many of the conclusions of this technique-see [12,33,3,5,17] for a modest sample of recent references-seem to be somewhat "incomplete." To make the distinction more explicit, let us consider the example of temperature-driven firstorder phase transition in the q-state Potts model with q ≫ 1.…”

Section: Introductionmentioning

confidence: 99%

Forbidden Gap Argument for Phase Transitions Proved by Means of Chessboard Estimates

Biskup¹,

Kotecký

2006

Commun. Math. Phys.

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Chessboard estimates are one of the standard tools for proving phase coexistence in spin systems of physical interest. In this note we show that the method not only produces a point in the phase diagram where more than one Gibbs states coexist, but that it can also be used to rule out the existence of shift-ergodic states that differ significantly from those proved to exist. For models depending on a parameter (say, the temperature), this shows that the values of the conjugate thermodynamic quantity (the energy) inside the "transitional gap" are forbidden in all shift-ergodic Gibbs states. We point out several models where our result provides useful additional information concerning the set of possible thermodynamic equilibria.

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“…Note that this does not violate the Mermin-Wagner theorem, as the symmetry being broken is not a continous one, but an additional discrete one. Meanwhile a mathematical proof is published about such type of models, 16 showing that such induced symmetry can be broken. In the classical nearest neighbor Heisenberg-model on the Kagome (CKLNNHM), all studies of the past are not consistent with a phase-transition at finite temperature.…”

Section: Introductionmentioning

confidence: 99%

ClassicalJ1-J2Heisenberg model on the kagome lattice

Spenke

Guertler

2012

Phys. Rev. B

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Motivated by earlier simulated annealing studies and materials with large spin on the Kagome lattice, we performed large scale parallel tempering simulations on the Kagome lattice for the extended classical Heisenberg model including next nearest neighbor interactions. We find that even a small inclusion of a J2 term induces anti-ferromagnetic order which prevails in the thermodynamic limit. The magnitude of this effect is surprising. While at J2 = 0 the finite-size behaviour does not suggest a phase-transition, at other points the numerical result is consistent with one. Close to J2 = 0 and for a positive sign of J2 two subsequent phase-transitions/crossovers are found, one of them connecting to the crossover for the J2 = 0 case, shedding light to the pure case. The universality classes of the transitions were explored.

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Order by Disorder, without Order, in a Two-Dimensional Spin System with O(2) Symmetry

Cited by 20 publications

References 41 publications

Quantum Spin Systems at Positive Temperature

Quantum Spin Systems at Positive Temperature

Forbidden Gap Argument for Phase Transitions Proved by Means of Chessboard Estimates

ClassicalJ1-J2Heisenberg model on the kagome lattice

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