The distributional zeta-function in disordered field theory

Svaiter, B. F.; Svaiter, N. F.

doi:10.1142/s0217751x1650144x

Cited by 18 publications

(23 citation statements)

References 69 publications

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“…(25), also with the large-N limit is quite natural and it is the only choice compatible with the method developed in Refs. [18,19]. In conclusion, our arguments stated here show the uniqueness of the solution for the problem of the structure in replica space.…”

Section: Spontaneous Symmetry Breaking In Replica Field Theorysupporting

confidence: 55%

“…An alternative approach to compute the average free energy of disordered systems was presented in Refs. [18,19]. We call it the distributional zeta-function method.…”

Section: From the Disordered Model To The Replica Field Theorymentioning

confidence: 99%

“…In this case, one is mainly interested in averaging the disorder-dependent free energy, which amounts to averaging the logarithm of the partition function. Recently, it was proposed an alternative method to average the disorder-dependent free energy [18,19]. In this approach, the dominant contribution to the average free energy is written as a series of the integer moments of the partition function of the model.…”

Section: Introductionmentioning

confidence: 99%

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Spontaneous symmetry breaking in replica field theory

et al. 2017

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In this paper we discuss a disordered d-dimensional Euclidean λϕ 4 model. The dominant contribution to the average free energy of this system is written as a series of the replica partition functions of the model. In each replica partition function, using the saddle-point equations and imposing the replica symmetric ansatz, we show the presence of a spontaneous symmetry breaking mechanism in the disordered model. Moreover, the leading replica partition function must be described by a large-N Euclidean replica field theory. We discuss finite temperature effects considering periodic boundary condition in Euclidean time and also using the Landau-Ginzburg approach. In the low temperature regime we prove the existence of N instantons in the model.

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Section: Spontaneous Symmetry Breaking In Replica Field Theorysupporting

confidence: 55%

“…An alternative approach to compute the average free energy of disordered systems was presented in Refs. [18,19]. We call it the distributional zeta-function method.…”

Section: From the Disordered Model To The Replica Field Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spontaneous symmetry breaking in replica field theory

et al. 2017

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“…See also Eqs. (28) and (29). For each k-th integer moment, E [Z l ], all the fields must be equal, we are led to the following choice in the structure of the fields in each…”

Section: Interacting Scalar Field In Euclidean Section Of the Schwarzmentioning

confidence: 99%

Multiplicative noise in Euclidean Schwarzschild manifold

Soares

Svaiter

Zarro

2020

Class. Quantum Grav.

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We discuss a λϕ 4 + ρϕ 6 scalar field model defined in the Euclidean section of the Schwarzschild solution of the Einstein equations in the presence of multiplicative noise. The multiplicative random noise is a model for fluctuations of the Hawking temperature. We adopt the standard procedure of averaging the noise dependent generating functional of connected correlation functions of the model. The dominant contribution to this quantity is represented by a series of the moments of the generating functional of correlation functions of the system. Positive and negative effective coupling constants appear in these integer moments. Fluctuations in the Hawking temperature are able to generate first-order phase transitions. Using the Gaussian approximation, we compute ϕ 2 for arbitrary values of the strength of the noise. Due to the presence of the multiplicative noise, we show that ϕ 2 near the horizon must be written as a series of the the renormalized two-point correlation functions associated to a free scalar field in Euclidean Rindler

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“…Recently, an alternative analytic calculation was proposed to compute the disorder average free-energy for the random source Landau-Ginzburg model [20,21]. The method that we named distributional zeta-function method (DZFM) shares similarities with the conventional replica method.…”

Section: Introductionmentioning

confidence: 99%

Disordered λφ4+ρφ6 Landau-Ginzburg model

et al. 2018

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We discuss a disordered λϕ 4 +ρϕ 6 Landau-Ginzburg model defined in a d-dimensional space. First we adopt the standard procedure of averaging the disorder dependent free energy of the model. The dominant contribution to this quantity is represented by a series of the replica partition functions of the system. Next, using the replica symmetry ansatz in the saddle-point equations, we prove that the average free energy represents a system with multiple ground states with different order parameters. For low temperatures we show the presence of metastable equilibrium states for some replica fields for a range of values of the physical parameters. Finally, going beyond the mean-field approximation, the one-loop renormalization of this model is performed, in the leading order replica partition function.

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The distributional zeta-function in disordered field theory

Cited by 18 publications

References 69 publications

Spontaneous symmetry breaking in replica field theory

Spontaneous symmetry breaking in replica field theory

Multiplicative noise in Euclidean Schwarzschild manifold

Disordered λφ4+ρφ6 Landau-Ginzburg model

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