Spontaneous versus explicit replica symmetry breaking in the theory of disordered systems

Mouhanna, D.; Tarjus, Gilles

doi:10.1103/physreve.81.051101

Cited by 13 publications

(22 citation statements)

References 64 publications

(197 reference statements)

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“…One must consider a generalization of the effective action where the scalar field is coupled linearly and quadratically to sources. [48,49,50,51,52]. Going back to our approach, for the latter terms, i.e., k > k c , although ϕ (k) = 0 is a local minimum, another global minimum appears for |λ 0 − kσ| > 4 √ 3 m 0 √ ρ 0 .…”

Section: Interacting Scalar Field In Euclidean Section Of the Schwarzmentioning

confidence: 90%

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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Section: Interacting Scalar Field In Euclidean Section Of the Schwarzmentioning

confidence: 90%

Multiplicative noise in Euclidean Schwarzschild manifold

Soares

Svaiter

Zarro

2020

Class. Quantum Grav.

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“…In a previous work 33 we have shown that the linear stability operator of the SD equations obtained from the 2-PI formalism is related to the "replicon" operator 34,35 which signals the instability of the replica-symmetric solution. In the present case where the self-energies are purely local, it is convenient to consider the 2-PI effective action Γ 2P I as a functional of the fields {φ a } and the self-energies {Σ ab } and study the stability of the stationary solutions by looking at the second derivatives of Γ 2P I with respect to the self-energies (see also [16,30] …”

Section: B Replicon Operator and Stabilitymentioning

confidence: 98%

“…We have kept nonzero sources J a that explicitly break the replica permutational symmetry in order to perform expansions in increasing number of free replica sum and access the (renormalized) disorderaveraged cumulants characterizing the system. 16,24,33 On the other hand, the sources K ab are set to zero to obtain Eq. (8).…”

Section: A Replicated Action and 2-pi Formalismmentioning

confidence: 99%

“…Taking advantage of the fact that the symmetry between replicas is explicitly broken by the sources, each component can then be expanded in free replica sums as done in previous work. 24,26,33 The details are given in Appendix A. Simplifications resulting from the large-N limit…”

Section: B Schwinger-dyson Equationsmentioning

confidence: 99%

“…As in [33] we introduce the longitudinal L (µ = ν = 1) and transverse T (µ = ν = 1) components of the 1-replica correlation function G…”

Section: -Pi Effective Actionmentioning

confidence: 99%

See 2 more Smart Citations

Phase diagram and criticality of the random anisotropy model in the large- N limit

Mouhanna

Tarjus

2016

Phys. Rev. B

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We revisit the thermodynamic behavior of the random-anisotropy O(N ) model by investigating its large-N limit. We focus on the system at zero temperature where the mean-field-like artifacts of the large-N limit are less severe. We analyze the connection between the description in terms of self-consistent Schwinger-Dyson equations and the functional renormalization group. We provide a unified description of the phase diagram and critical behavior of the model and clarify the nature of the possible "glassy" phases. Finally we discuss the implications of our findings for the finite-N and finite-temperature systems.

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Hierarchical reference theory of critical fluids in disordered porous media

et al. 2011

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We consider the equilibrium behavior of fluids imbibed in disordered mesoporous media, including their gas-liquid critical point when present. Our starting points are on the one hand a description of the fluid/solid-matrix system as a quenched-annealed mixture and on the other hand the Hierarchical Reference Theory (HRT) developed by A. Parola and L. Reatto to cope with density fluctuations on all length scales. The formalism combines liquid-state statistical mechanics and the theory of systems in the presence of quenched disorder. A straightforward implementation of the HRT to the quenched-annealed mixture is shown to lead to unsatisfactory results, while indicating that the critical behavior of the system is in the same universality class as that of the random-field Ising model. After a detour via the field-theoretical renormalization group approach of the latter model, we finally lay out the foundations for a proper HRT of fluids in a disordered porous material.

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Spontaneous versus explicit replica symmetry breaking in the theory of disordered systems

Cited by 13 publications

References 64 publications

Multiplicative noise in Euclidean Schwarzschild manifold

Multiplicative noise in Euclidean Schwarzschild manifold

Phase diagram and criticality of the random anisotropy model in the large- N limit

Hierarchical reference theory of critical fluids in disordered porous media

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