Sherrington-Kirkpatrick model for spin glasses: Solution via the distributional zeta function method

Use of the surrogate zeta-function method was crucial in calculating the Casimir energy in non-Abelian Kaluza–Klein theories. We establish the validity of this method for the case where the background metric is (Euclidean space) × (N sphere). Our techniques do not apply to the case where the background is (Minkowski space) × (N sphere).

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Some comments on the Sherrington-Kirkpatrick model of spin glasses

Communications in Mathematical Physics ◽

10.1007/bf01225372 ◽

1987 ◽

Vol 112 (4) ◽

pp. 553-566 ◽

Cited By ~ 28

Author(s):

J. Fröhlich ◽

B. Zegarlinski

Keyword(s):

Spin Glasses ◽

Kirkpatrick Model

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Thermal Properties of the One-Dimensional Duffin–Kemmer–Petiau Oscillator Using Hurwitz Zeta Function

Zeitschrift für Naturforschung A ◽

10.1515/zna-2015-0191 ◽

2015 ◽

Vol 70 (10) ◽

pp. 867-874 ◽

Cited By ~ 7

Author(s):

Abdelamelk Boumali

Keyword(s):

Free Energy ◽

Thermal Properties ◽

Zeta Function ◽

Function Method ◽

Vacuum Expectation ◽

Vacuum Expectation Value ◽

Hurwitz Zeta Function ◽

Expectation Value ◽

One Dimensional ◽

The One

AbstractIn this paper, we investigated the thermodynamics properties of the one-dimensional Duffin–Kemmer–Petiau oscillator by using the Hurwitz zeta function method. In particular, we calculated the following main thermal quantities: the free energy, the total energy, the entropy, and the specific heat. The Hurwitz zeta function allowed us to compute the vacuum expectation value of the energy of our oscillator.

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The zeta function method and the harmonic oscillator propagator

American Journal of Physics ◽

10.1119/1.1311784 ◽

2001 ◽

Vol 69 (2) ◽

pp. 232-235 ◽

Cited By ~ 6

Author(s):

F. A. Barone ◽

C. Farina

Keyword(s):

Harmonic Oscillator ◽

Zeta Function ◽

Function Method

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Is the Sherrington–Kirkpatrick model relevant for real spin glasses?

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8113/41/32/324016 ◽

2008 ◽

Vol 41 (32) ◽

pp. 324016 ◽

Cited By ~ 8

Author(s):

A P Young

Keyword(s):

Spin Glasses ◽

Kirkpatrick Model

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Equivalence of zeta function technique and Abel–Plana formula in regularizing the Casimir energy of hyper-rectangular cavities

Modern Physics Letters A ◽

10.1142/s0217732314501818 ◽

2014 ◽

Vol 29 (35) ◽

pp. 1450181

Author(s):

Rui-Hui Lin ◽

Xiang-Hua Zhai

Keyword(s):

Zeta Function ◽

Regularization Method ◽

Function Method ◽

Casimir Energy ◽

Function Technique ◽

Massless Scalar ◽

Massless Scalar Field ◽

Epstein Zeta Function ◽

Formula Method ◽

Reflection Formula

Zeta function regularization is an effective method to extract physical significant quantities from infinite ones. It is regarded as mathematically simple and elegant but the isolation of the physical divergency is hidden in its analytic continuation. By contrast, Abel–Plana formula method permits explicit separation of divergent terms. In regularizing the Casimir energy for a massless scalar field in a D-dimensional rectangular box, we give the rigorous proof of the equivalence of the two methods by deriving the reflection formula of Epstein zeta function from repeatedly application of Abel–Plana formula and giving the physical interpretation of the infinite integrals. Our study may help with the confidence of choosing any regularization method at convenience among the frequently used ones, especially the zeta function method, without the doubts of physical meanings or mathematical consistency.

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