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Schor, Ricardo S.; O’Carroll, Michael

doi:10.1023/a:1018688722554

Cited by 36 publications

(30 citation statements)

References 9 publications

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“…It is important to stress that in [2,3] the spectral results for N = 1 were obtained for the complete model, providing an extension beyond the ladder approximation, and that the same procedure also applies to extend the spectral results from [4] and ours, i.e. for the N > 1 case, to the full model.…”

Section: Discussionmentioning

confidence: 84%

Transfer Matrix Spectrum for O(N) High Temperature Lattice Classical Ferromagnetic Spin Systems and Staggering Transformations

Anjos¹,

Veiga²,

O’Carroll³

2005

Phys. Scr.

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We obtain the low-lying energy-momentum spectrum for the imaginary-time lattice quantum field model associated with d-dimensional lattice ferromagnetic classical N -component vector spin systems at high temperature (0 < β 1). Each system is characterized by a single site "a priori" spin probability distribution. The energy-momentum spectrum exhibits isolated dispersion curves which are identified as single particles and multi-particle bands. Our two-particle bound state analysis is restricted to a ladder approximation of the Bethe-Salpeter equation, and the existence of bound states depend on whether or not Gaussian domination for the four-point function is verified. It is known that two-particle bound states appear below the two-particle band if Gaussian domination does not hold. Here, we show that two two-particle bound states appear above the two-particle band if Gaussian domination is verified. We also show how the complete two-particle spectral pattern for these models can be understood by making a correspondence between the Bethe-Salpeter equation and a two-particle lattice Schrödinger Hamiltonian operator with attractive or repulsive spin-dependent delta potentials at the origin. A staggering transformation is used to relate the attractive and repulsive potential cases, as well as their associated Hamiltonians spectrum and eigenfunctions.

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Section: Discussionmentioning

confidence: 84%

Transfer Matrix Spectrum for O(N) High Temperature Lattice Classical Ferromagnetic Spin Systems and Staggering Transformations

Anjos¹,

Veiga²,

O’Carroll³

2005

Phys. Scr.

Self Cite

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“…Já na mecânica estatística de sistemas fora do equilíbrio que adimitem uma dinâmica markoviana [2], o espectro do gerador da dinâmica, corresponde ao gerador do semi-grupo contínuo de evolução no tempo para o problema e determina a taxa com a Dada uma função F ( s 1 ... s j ) dos campos, a média ou valor médio normalizado dessa função é definida por: (ver [6,7]). A aplicabilidade do modelo de spins O(N ) a uma variedade tão grande de modelos nas proximidades de um ponto crítico é a manifestação da universalidade em fenômenos críticos (ver [7,8] [9,10,11,12] foram obtidas propriedades análogas as demonstradas aqui. O trabalho feito aqui, está sintetizado na referência [13].…”

Section: O Modelo O(n ) E Uma Estratégia Para a Determinação Do Especunclassified

“…Este parâmetro caracteriza a ssd, e pode ser utilizado para indexar os casos atrativos (α N > 0, subjulgação gaussiana e estados ligados abaixo da banda) e repulsivos ( α N < 0, dominação gaussiana e estados ligados acima da banda). Antes de encerrarmos essa sessão , destacamos que é possível estender 9 Essa exigência garante também que a massa de uma partícula seja a mesma esses resultados além da aproximação escada, como foi mostrado para o caso do modelo de spin escalar nas referencias [11] e [12].…”

Section: Estados Ligados De Duas Partículasunclassified

“…Para tanto utilizamos as ferramentas desenvolvidas em [2] para a análise da equação de Bethe-Salpeter na rede. Nossa análise é similar a feita nas referências [10], [11] e [12] para o modelo de spins escalar (O(1)). Como em [15], nós estabelecemos condições para a existência de estados de duas partículas ligadas e estabelecemos a energia de ligação.…”

Section: Definimos a Transformção De Staggering Porunclassified

“…No entanto, a análise feita aqui estende os resultados anteriores por tratar o caso de dominação gaussiana (α N < 0) e analisar propriedades de simetria entre os casos de dominação e subjulgação gaussiana. É importante destacar que em [11,12] as propriedades espectrais para o sistema de spins escalares (N = 1) foram obtidos para o "modelo completo", fornecendo uma extensão que vai além da aproximação em …”

Section: Definimos a Transformção De Staggering Porunclassified

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"Espectro de excitação para modelos quânticos na rede"

Anjos¹

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Uma transformação de staggering é utilizada para relacionar os casos de potenciais atrativos e repulsivos e o espectro dos hamiltonianos e suas autofunções. system is characterized by a single site "a priori" spin probability distribution. We work only at high temperature region (0 < β 1). The energy-momentum spectrum exhibits isolated dispersion curves which are identified as single particles and multiparticle bands. In particular, we study states of one and two-particles.For the single particle spectrum, we obtain the dispersion curve and the

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Scattering and Bound States in Euclidean Lattice Quantum Field Theories

Auil¹,

Barata²

2001

Ann. Henri Poincaré

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In this paper we study the property of asymptotic completeness in (massive) Euclidean lattice quantum field theories. We use the methods of Spencer and Zirilli [2] to prove, under suitable hypothesis, two-body asymptotic completeness, i.e., for the energy range just above the two-particle threshold.This paper is dedicated to the problem of asymptotic completeness (AC) in Euclidean lattice quantum field theories. In our analysis we followed closely the methods of Spencer and Zirilli [2], who proved, probably for the first time, asymptotic completeness for a true relativistic quantum field theoretical model for a limited range of energies. In spite of the higher technical difficulties posed by the lack of Lorentz invariance and other problems we are able to reproduce the same results of [2] in our lattice context. We have namely proven two-body asymptotic completeness, i.e., asymptotic completeness up to energies just above the two-particle threshold. These methods rely basically on the exponential decay of the Bethe-Salpeter kernel in space variables, and can be applied to the analysis of bound states and resonances for weakly coupled models, as in [15,16] in the continuum, or [44,47,45,46] in lattice models. Also, and with more work, the methods can be extended to the analysis of three-particle bound states and AC following, for instance, [17] and [13], respectively. Limitations on the energy range are found, unfortunately, in all the proofs of asymptotic completeness performed along these lines on the continuum. This deplorable state of affairs urges the QFT community to develop new ideas and techniques to deal with the spectral problems of QFT, but this is not our subject here. See, however, [8] (and also [9, 10]) for a proposal involving the nuclearity criterion. For a discussion of the problem of asymptotic completeness in QED in the context of perturbation theory, see [11].We believe our results are interesting not only due to their connection to QFT problems, as mentioned above. Some of the models we consider are, in fact, models of classical statistical mechanical spin systems (for instance, the Ising model) and the spectral properties of the transfer matrix reflect on corrections to the exponential decay of correlations as, for instance, the Ornstein-Zernike corrections (see [22,33,34,35]).In our work many adaptations to the lattice context were necessary, which increased considerably the technical complications involved. Let us briefly discuss some of them. In their work, for instance, Spencer and Zirilli [2] restricted a good part of their analysis to the zero-momentum sector of the energy-momentum spectrum and then invoked Lorentz covariance to extend their results to nonzero momenta. This strategy of argumentation simplifies many computations but cannot be applied to a situation where Lorentz covariance is lacking. Another major source of complications involved a series of space-time changes of variables intended to express some four point functions and the Bethe-Salpeter kernel in terms of "centre of...

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Cited by 36 publications

References 9 publications

Transfer Matrix Spectrum for O(N) High Temperature Lattice Classical Ferromagnetic Spin Systems and Staggering Transformations

Transfer Matrix Spectrum for O(N) High Temperature Lattice Classical Ferromagnetic Spin Systems and Staggering Transformations

"Espectro de excitação para modelos quânticos na rede"

Scattering and Bound States in Euclidean Lattice Quantum Field Theories

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