Disordered 
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 Landau-Ginzburg model

Díaz, Rodolfo A.; Svaiter, N. F.; Krein, G.; Zarro, C. A. D.

doi:10.1103/physrevd.97.065017

Cited by 10 publications

(10 citation statements)

References 55 publications

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“…In this appendix we review the alternative approach to compute the configurational average of the free energy of disordered systems presented in [42][43][44]. We begin with the definition of the generalized ζ-function given by…”

Section: (A14)mentioning

confidence: 99%

“…Recently, it has been proposed an alternative method to average the disorder-dependent free energy in statistical field theory called the distributional zeta function method (DZFM) [42]. Within this approach, the dominant contribution to the average free energy is expressed as a series of the integer moments of the partition function of the model [43][44][45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

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The Sherrington-Kirkpatrick model for spin glasses: A new approach for the solution

Rodríguez-Camargo,

Mojica-Nava,

Svaiter

2021

Preprint

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We discuss the Sherrington-Kirkpatrick mean-field version of a spin glass within the distributional zeta-function method (DZFM). In the DZFM, since the dominant contribution to the average free energy is written as a series of moments of the partition function of the model, the spin-glass multivalley structure is obtained. Also, an exact expression for the saddle points corresponding to each valley and a global critical temperature showing the existence of many stables or at least metastables equilibrium states is presented. Near the critical point we obtain analytical expressions of the order parameters that are in agreement with phenomenological results. We evaluate the linear and nonlinear susceptibility and we find the expected singular behavior at the spin-glass critical temperature. Furthermore, we obtain a positive definite expression for the entropy and we show that ground-state entropy tends to zero as the temperature goes to zero. We show that our solution is stable for each term in the expansion. Finally, we analyze the behavior of the overlap distribution, where we find a general expression for each moment of the partition function.

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Section: (A14)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Sherrington-Kirkpatrick model for spin glasses: A new approach for the solution

Rodríguez-Camargo,

Mojica-Nava,

Svaiter

2021

Preprint

View full text Add to dashboard Cite

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“…An application of such procedure was presented in Ref. [33,34] where a Landau-Ginzburg model with a disorder field linearly and quadratically coupled with the order parameter was discussed. The static version of a non-relativistic field theory with a complex field was investigated in [35].…”

Section: Introductionmentioning

confidence: 99%

Directed Polymers and Interfaces in Disordered Media

2020

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We consider field theory formulation for directed polymers and interfaces in the presence of quenched disorder. We write a series representation for the averaged free energy, where all the integer moments of the partition function of the model contribute. The structure of field space is analysed for polymers and interfaces at finite temperature using the saddle-point equations derived from each integer moments of the partition function. For the case of an interface we obtain the wandering exponent ξ = ( 4 − d ) / 2 , also obtained by the conventional replica method for the replica symmetric scenario.

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“…We use this fact to generate objects where each subsystem of a complete graph is contributing to improve the network performance measure. The DZF method has been used successfully to study the Landau-Ginzburg approach in replica field theory [59], the disordered λϕ 4 +ρϕ 6 Landau-Ginzburg model [60], disordered Bose-Einstein condensate in hard walls trap [61], multiplicative noise in Euclidean Schwarzschild manifold [62], and more recently for polymers in random media [63]. Furthermore, it has been mentioned its potential for entanglement networks in random media [64].…”

Section: Introductionmentioning

confidence: 99%

Systemic Performance Measures from Distributional Zeta-Function

Rodríguez-Camargo,

Urquijo-Rodríguez,

Mojica-Nava

2020

Preprint

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We propose the use of the Distributional Zeta-Function (DZF) for constructing a new set of Systemic Performance Measures (SPM). SPM have been proposed to investigate network synthesis problems such as the growing of linear consensus networks. The adoption of the DZF has shown interesting physical consequences that in the usual replica method are still unclarified, i.e., the connection between the spontaneous symmetry breaking mechanism and the structure of the replica space in the disordered model. We relate topology of the network and the partition function present in the DZF by using the spectral and the Hamiltonian structure of the system. The studied objects are the generalized partition funcion, the DZF, the Expected value of the replica partition function, and the quenched free energy of a field network. We show that with these objects we need few operations to increase the percentage of performance enhancement of a network. Furthermore, we evalue the location of the optimal added links for each new SPM and calculate the performance improvement of the new network for each new SPM via the spectral zeta function, H2-norm, and the communicability between nodes. We present the advantages of this new set of SPM in the network synthesis and we propose other methods for using the DZF to explore some issues such as disorder, critical phenomena, finite-temperature, and finite-size effects on networks. Relevance of the results are discussed.

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Disordered λφ4+ρφ6 Landau-Ginzburg model

Cited by 10 publications

References 55 publications

The Sherrington-Kirkpatrick model for spin glasses: A new approach for the solution

The Sherrington-Kirkpatrick model for spin glasses: A new approach for the solution

Directed Polymers and Interfaces in Disordered Media

Systemic Performance Measures from Distributional Zeta-Function

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