Spontaneous symmetry breaking in replica field theory

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

doi:10.1103/physrevd.96.065012

Cited by 12 publications

(19 citation statements)

References 88 publications

(87 reference statements)

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“…The basic quantity is a distributional zetafunction. Within such a framework it has been verified the presence of a spontaneous symmetry breaking mechanism in a disordered d-dimensional Euclidean λϕ 4 model [54]. In addition, in the low temperature regime the existence of N instantons in such a model has been confirmed.…”

Section: Discussionmentioning

confidence: 69%

Entanglement dynamics in random media

2017

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We study how the entanglement dynamics between two-level atoms is impacted by random fluctuations of the light cone. In our model the two-atom system is envisaged as an open system coupled with an electromagnetic field in the vacuum state. We employ the quantum master equation in the Born-Markov approximation in order to describe the completely positive time evolution of the atomic system. We restrict our investigations to the situation in which the atoms are coupled individually to two spatially separated cavities, one of which displaying the emergence of light-cone fluctuations. In such a disordered cavity, we assume that the coefficients of the Klein-Gordon equation are random functions of the spatial coordinates. The disordered medium is modeled by a centered, stationary and Gaussian process. We demonstrate that disorder has the effect of slowing down the entanglement decay. We conjecture that in a strong disorder environment the mean life of entangled states can be enhanced in such a way as to almost completely suppress quantum nonlocal decoherence.Comment: Accepted for publication in Physical Review

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Section: Discussionmentioning

confidence: 69%

Entanglement dynamics in random media

2017

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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%

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

Rodríguez-Camargo,

Mojica-Nava,

Svaiter

2021

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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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“…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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Spontaneous symmetry breaking in replica field theory

Cited by 12 publications

References 88 publications

Entanglement dynamics in random media

Entanglement dynamics in random media

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

Directed Polymers and Interfaces in Disordered Media

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