Small-cluster renormalization group in Ising and Blume-Emery-Griffiths models with ferromagnetic, antiferromagnetic, and quenched disordered magnetic interactions

Antenucci, Fabrizio; Crisanti, A.; Leuzzi, Luca

doi:10.1103/physreve.90.012112

Cited by 6 publications

(5 citation statements)

References 45 publications

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“…To include the role of the leakages and the evolution of the mode amplitudes, a series of recent works 28,55,70 have considered the application of the replica method to the general Hamiltonian Eq. (23).…”

Section: Results For the General Hamiltonian Modelmentioning

confidence: 99%

“…In the following we consider the symmetrized probability distribution P (|C|), without any loss of generality. It can be shown 70 that for m = 0 it holds simply C ab = Q 2 ab , so that the intensity fluctuations overlap is nontrivial in the RL regime and the replica symmetry breaking can be studied from intensity spectrum data. We note also that instead, for low disorder, at the IW-ML transition C ab does not change at the transition 70 .…”

Section: Results For the General Hamiltonian Modelmentioning

confidence: 99%

“…It can be shown 70 that for m = 0 it holds simply C ab = Q 2 ab , so that the intensity fluctuations overlap is nontrivial in the RL regime and the replica symmetry breaking can be studied from intensity spectrum data. We note also that instead, for low disorder, at the IW-ML transition C ab does not change at the transition 70 . A typical scenario for the overlap C in an open cavity for high disorder is shown in Fig.…”

Section: Results For the General Hamiltonian Modelmentioning

confidence: 99%

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Statistical mechanics models for multimode lasers and random lasers

Antenucci

Crisanti

Ibáñez-Berganza

et al. 2016

Philosophical Magazine

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We review recent statistical mechanical approaches to multimode laser theory. The theory has proved very effective to describe standard lasers. We refer of the mean field theory for passive mode locking and developments based on Monte Carlo simulations and cavity method to study the role of the frequency matching condition. The status for a complete theory of multimode lasing in open and disordered cavities is discussed and the derivation of the general statistical models in this framework is presented. When light is propagating in a disordered medium, the system can be analyzed via the replica method. For high degrees of disorder and nonlinearity, a glassy behavior is expected at the lasing threshold, providing a suggestive link between glasses and photonics. We describe in details the results for the general Hamiltonian model in mean field approximation and mention an available test for replica symmetry breaking from intensity spectra measurements. Finally, we summary some perspectives still opened for such approaches.Comment: 16 pages, 7 figure

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Section: Results For the General Hamiltonian Modelmentioning

confidence: 99%

Section: Results For the General Hamiltonian Modelmentioning

confidence: 99%

Section: Results For the General Hamiltonian Modelmentioning

confidence: 99%

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Statistical mechanics models for multimode lasers and random lasers

Antenucci

Crisanti

Ibáñez-Berganza

et al. 2016

Philosophical Magazine

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“…The phase diagram of the spin-1 BEG model was studied by mean field evaluations (see, for example, Refs. [53,54,66]), in renormalization-group analyses [67][68][69], with The blue dots represent a first order transition line from the antiferromagnetic state to a paramagnetic state with lower values of q, and the green dots depict the first order transition line in the paramagnetic state, also from a higher to a lower value of q. CP is a critical point and CE is the critical end point. The gray curves connect states with fixed q-values.…”

Section: Appendix F: Beg-phase-diagrammentioning

confidence: 99%

Bad metal and negative compressibility transitions in a two-band Hubbard model

Fresard,

Steffen,

Kopp

2022

Preprint

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We analyze the paramagnetic state of a two-band Hubbard model with finite Hund's coupling close to integer filling at n = 2 in two spacial dimensions. Previously, a Mott metal-insulator transition was established at n = 2 with a coexistence region of a metallic and a bad metal state in the vicinity of that integer filling. The coexistence region ends at a critical point beyond which a charge instability persists. Here we investigate the transition into negative electronic compressibility states for an extended filling range close to n = 2 within a slave boson setup. We analyze the separate contributions from the (fermionic) quasiparticles and the (bosonic) multiparticle incoherent background and find that the total compressibility depends on a subtle interplay between the quasiparticle excitations and collective fields. Implementing a Blume-Emery-Griffiths model approach for the slave bosons, which mimics the bosonic fields by Ising-like pseudospins, we suggest a feedback mechanism between these fields and the fermionic degrees of freedom. We argue that the negative compressibility can be sustained for heterostructures of such strongly correlated planes and results in a large capacitance of these structures. The strong density dependence of these capacitances allows to tune them through small electronic density variations. Moreover, by resistive switching from a Mott insulating state to a metallic state through short electric pulses, transitions between fairly different capacitances are within reach. I. INTRODUCTION.

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“…These properties have been observed in the mean-field approximation, where the self-consistent solution for the spin-glass phase is computed in the full replica symmetry breaking (RSB) Parisi ansatz [21] and on the cubic 3D lattice with nearest-neighbor couplings [22,23]. The frustrated BEG model has been studied by means of numerical renormalization group techniques, as well, with results depending on the underlying lattice and the renormalization technique adopted [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Dynamical arrest with zero complexity: The unusual behavior of the spherical Blume-Emery-Griffiths disordered model

Rainone¹,

Paoluzzi²,

Leuzzi³

2015

Phys. Rev. E

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The short- and long-time dynamics of model systems undergoing a glass transition with apparent inversion of Kauzmann and dynamical arrest glass transition lines is investigated. These models belong to the class of the spherical mean-field approximation of a spin-1 model with p-body quenched disordered interaction, with p>2, termed spherical Blume-Emery-Griffiths models. Depending on temperature and chemical potential the system is found in a paramagnetic or in a glassy phase and the transition between these phases can be of a different nature. In specific regions of the phase diagram coexistence of low-density and high-density paramagnets can occur, as well as the coexistence of spin-glass and paramagnetic phases. The exact static solution for the glassy phase is known to be obtained by the one-step replica symmetry breaking ansatz. Different scenarios arise for both the dynamic and the thermodynamic transitions. These include: (i) the usual random first-order transition (Kauzmann-like) for mean-field glasses preceded by a dynamic transition, (ii) a thermodynamic first-order transition with phase coexistence and latent heat, and (iii) a regime of apparent inversion of static transition line and dynamic transition lines, the latter defined as a nonzero complexity line. The latter inversion, though, turns out to be preceded by a dynamical arrest line at higher temperature. Crossover between different regimes is analyzed by solving mode-coupling-theory equations near the boundaries of paramagnetic solutions and the relationship with the underlying statics is discussed.

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Small-cluster renormalization group in Ising and Blume-Emery-Griffiths models with ferromagnetic, antiferromagnetic, and quenched disordered magnetic interactions

Cited by 6 publications

References 45 publications

Statistical mechanics models for multimode lasers and random lasers

Statistical mechanics models for multimode lasers and random lasers

Bad metal and negative compressibility transitions in a two-band Hubbard model

Dynamical arrest with zero complexity: The unusual behavior of the spherical Blume-Emery-Griffiths disordered model

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