Thermodynamics of the bosonic randomized Riemann gas

Dueñas, Jesús García de; Svaiter, N. F.

doi:10.1088/1751-8113/48/31/315201

Cited by 3 publications

(3 citation statements)

References 39 publications

(57 reference statements)

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“…Disordered systems have been investigated for decades in statistical mechanics [1][2][3][4][5], condensed matter, gravitational physics [6][7][8][9][10][11] and even number theory [12]. The physics of spin glasses, disordered electronic systems and directed polymers in random media are well known examples of such systems.…”

Section: Introductionmentioning

confidence: 99%

The distributional zeta-function in disordered field theory

Svaiter

2016

Int. J. Mod. Phys. A

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In this paper we present a new mathematical rigorous technique for computing the average free energy of a disordered system with quenched randomness, using the replicas. The basic tool of this technique is a distributional zeta-function, a complex function whose derivative at the origin yields the average free energy of the system as the sum of two contributions: the first one is a series in which all the integer moments of the partition function of the model contribute; the second one, which can not be written as a series of the integer moments, can be made as small as desired. This result supports the use of integer moments of the partition function, computed via replicas, for expressing the average free energy of the system. One advantage of the proposed formalism is that it does not require the understanding of the properties of the permutation group when the number of replicas goes to zero. Moreover, the symmetry is broken using the saddle-point equations of the model. As an application for the distributional zeta-function technique, we obtain the average free energy of the disordered λϕ 4 model defined in a d-dimensional Euclidean space. keywords: disordered systems; average free-energy; replicas; distributional zeta-function.

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Section: Introductionmentioning

confidence: 99%

The distributional zeta-function in disordered field theory

Svaiter

2016

Int. J. Mod. Phys. A

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“…A classical example of such system is a bosonic Riemann gas, a second quantized mechanical system at temperature β −1 with partition function given by the Riemann zeta-function. Recently, it was discussed connections between the non-trivial zeros of the Riemann zeta-function and the behavior of the thermodynamic free energy of a disordered system using the arithmetic bosonic gas with quenched disorder [20]. Introducing randomness in the bosonic Riemann gas and studying the thermodynamic variables of this arithmetic gas in the complex β-plane, the connection between the zeros of the Riemann zeta-function and physics was established.…”

Section: Introductionmentioning

confidence: 99%

Functional equations for regularized zeta-functions and diffusion processes

Saldivar

Svaiter

Zarro

2020

J. Phys. A: Math. Theor.

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We discuss modifications in the integral representation of the Riemann zetafunction that lead to generalizations of the Riemann functional equation that preserves the symmetry s → (1 − s) in the critical strip. By modifying one integral representation of the zeta-function with a cut-off that does exhibit the symmetry x → 1/x, we obtain a generalized functional equation involving Bessel functions of second kind. Next, with another cut-off that does exhibit the same symmetry, we obtain a generalization for the functional equation involving only one Bessel function of second kind. Some connection between one regularized zeta-function and the Laplace transform of the heat kernel for the Euclidean and hyperbolic space is discussed.

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“…Disordered systems have been investigated for decades in statistical mechanics [1][2][3][4][5], gravitational physics [6][7][8][9][10][11], number theory [12] and condensed matter. For the case of disordered systems with quenched disorder, one is mainly interested in averaging the free energy over the disorder, which amounts to averaging the log of the partition function Z.…”

mentioning

confidence: 99%

Disordered Field Theory in $d=0$ and Distributional Zeta-Function

Svaiter,

Svaiter

2016

Preprint

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Recently we introduced a new technique for computing the average free energy of a system with quenched randomness. The basic tool of this technique is a distributional zeta-function. The distributional zeta-function is a complex function whose derivative at the origin yields the average free energy of the system as the sum of two contributions: the first one is a series in which all the integer moments of the partition function of the model contribute; the second one, which can not be written as a series of the integer moments, can be made as small as desired. In this paper we present a mathematical rigorous proof that the average free energy of one disordered λϕ 4 model defined in a zero-dimensional space can be obtained using the distributional zeta-function technique. We obtain an analytic expression for the average free energy of the model.

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Thermodynamics of the bosonic randomized Riemann gas

Cited by 3 publications

References 39 publications

The distributional zeta-function in disordered field theory

The distributional zeta-function in disordered field theory

Functional equations for regularized zeta-functions and diffusion processes

Disordered Field Theory in $d=0$ and Distributional Zeta-Function

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