878 research outputs found
Universality and deviations in disordered systems
No full textWe compute the probability of positive large deviations of the free energy per spin in mean-field spin-glass models. The probability vanishes in the thermodynamic limit as P (Delta f) proportional to exp[-N(2)L(2)(Delta f)]. For the Sherrington-Kirkpatrick model we find L(2)(Delta f)=O(Delta f)(12/5) in good agreement with numerical data and with the assumption that typical small deviations of the free energy scale as N(1/6). For the spherical model we find L(2)(Delta f) =O(Delta f)(3) in agreement with recent findings on the fluctuations of the largest eigenvalue of random Gaussian matrices. The computation is based on a loop expansion in replica space and the non-Gaussian behavior follows in both cases from the fact that the expansion is divergent at all orders. The factors of the leading order terms are obtained resumming appropriately the loop expansion and display universality, pointing to the existence of a single universal distribution describing the small deviations of any model in the full-replica-symmetry-breaking class
Phase diagram and large deviations in the free energy of mean-field spin glasses
No full textWe consider the probability distribution of large deviations in the spin-glass free energy for the Sherrington-Kirkpatrick mean-field model, i.e., the exponentially small probability of finding a system with intensive free energy smaller than the most likely one. This result is obtained by computing Phi(n,T)=TZ(n)/n, i.e., the average value of the partition function to the power n as a function of n. We study in full details the phase diagram of Phi(n,T) in the (n,T) plane computing in particular the stability of the replica-symmetric solution. At low temperatures we compute Phi(n,T) in series of n and tau=T(c)-T at high orders using the standard hierarchical ansatz and confirm earlier findings on the O(n(5)) scaling. We prove that the O(n(5)) scaling is valid at all orders and obtain an exact expression for the coefficient in term of the function q(x). Resumming the series we obtain the large deviations probability at all temperatures. At zero temperature the analytical prediction displays a remarkable quantitative agreement with the numerical data. A similar computation for the simpler spherical model is also performed and the connection between large and small deviations is discussed
Large deviations of the free energy in diluted mean-field spin-glass
No full textSample-to-sample free-energy fluctuations in spin-glasses display a markedly different behaviour in finite-dimensional and fully connected models, namely Gaussian versus non-Gaussian. Spin-glass models defined on various types of random graphs are in an intermediate situation between these two classes of models and we investigate whether the nature of their free-energy fluctuations is Gaussian or not. It has been argued that Gaussian behaviour is present whenever the interactions are locally non-homogeneous, i.e. in most cases with the notable exception of models with fixed connectivity and random couplings J(ij) = +/-(J) over tilde. We confirm these expectations by means of various analytical results concerning the large deviations of the free energy. In particular we unveil the connection between the spatial fluctuations of the populations of fields defined at different sites of the lattice and the Gaussian nature of the free-energy fluctuations. In contrast, on locally homogeneous lattices the populations do not fluctuate over the sites and as a consequence the small deviations of the free energy are non-Gaussian and scale as in the Sherrington-Kirkpatrick model
Zero-temperature limit of the supersymmetry-breaking complexity in dilute spin-glass models
No full textWe study the supersymmetry (SUSY)-breaking complexity of the Bethe lattice spin-glass in the zero temperature limit. We consider both the Gaussian and the bimodal distribution of the coupling constants. For J(ij)=+/- 1 the SUSY breaking theory yields field distributions that concentrate on integer values at low temperatures, at variance with the unbroken SUSY theory. This concentration takes place both in the quenched as well as in the simpler annealed formulation
Chaos in temperature in the Sherrington-Kirkpatrick model
No full textWe prove the existence of chaos in temperature in the Sherrington-Kirkpatrick model. The effect is exceedingly small, namely, of the ninth order in perturbation theory. The equations describing two systems at different temperatures constrained to have a fixed overlap are studied analytically and numerically, yielding information about the behavior of the overlap distribution function P_(T1,T2)(q) in finite-size systems
Analysis of the ∞-replica symmetry breaking solution of the Sherrington-Kirkpatrick model
No full textIn this work we analyze the Parisi ∞-replica symmetry breaking solution of the Sherrington-Kirkpatrick model without external field using high order perturbative expansions. The predictions are compared with those obtained from the numerical solution of the ∞-replica symmetry breaking equations, which are solved using a pseudospectral code that allows for very accurate results. With these methods we are able to get more insight into the analytical properties of the solutions. We are also able to determine numerically the end point x_max of the plateau of q(x) and find that limopT⃗0 x_max(T)>0.5
Chaos in temperature in diluted mean-field spin-glass
No full textWe consider the problem of temperature chaos in mean-field spin-glass models defined on random lattices with finite connectivity. By means of an expansion in the order parameter we show that these models display a much stronger chaos effect than the fully connected Sherrington-Kirkpatrick model with the exception of the Bethe lattice with a bimodal distribution of the couplings
Rare location of facial osteoma
No full textOsteomas are slow growing benign bone tumors that frequently occur in the craniofacial area. So far eight cases have been reported in English literature to be located along the zygomatic arch. A case of a rapid growth hard swelling bone mass of a Caucasian 69-year-old male is reported. The developing facial asymmetry was the main concern of the patient that had no other symptoms. Computed tomography imaging showed a bone density growing mass located on the lateral side of the right zygomatic arch, about at the temporozygomatic suture, in close relation with the facial nerve temporo-zygomatic branch. Under general anesthesia, via a hemi-coronal approach, the bone mass was removed and the resulting defect was closed with a homologous parietal bone graft. Immediately after the intervention no facial asymmetry was evident, with a House-Brackmann facial nerve grading system scale value of 1. Three months after the intervention no recurrence was evident. Facial osteomas of the zygomatic arch are rare but due to their location, like the case reported here, they can be a challenge for the surgeon for both aesthetic and functional outcomes, and a major concern for the patient. Despite their simple diagnosis, no recurrence is evident, major efforts have to be made while planning a safe surgical excision
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