arXiv subjects

Paola Ranieri

Publications and source records attributed to Paola Ranieri.

4 recordsLinked to original sources

arXiv1998

Finite dimensional corrections to mean field in a short-range p-spin glassy model

In this work we discuss a short range version of the $p$-spin model. The model is provided with a parameter that allows to control the crossover with the mean field behaviour. We detect a discrepancy between the perturbative approach and numerical simulation. We attribute it to non-perturbative effects due to the finite probability that each particular realization of the disorder allows for the formation of regions where the system is less frustrated and locally freezes at a higher temperature.

cond-mat.dis-nn↗

arXiv1997

Dynamical fluctuations in an exactly solvable model of spin glasses

In this work we calculate the dynamical fluctuations at O(1/N) in the low temperature phase of the $p=2$ spherical spin glass model. We study the large-times asymptotic regimes and we find, in a short time-differences regime, a fluctuation dissipation relation for the four-point correlation functions. This relation can be extended to the out of equilibrium regimes introducing a function $X_{t}$ which, for large time $t$, we find scales as $t^{-1/2}$ as in the case of the two-point functions.

cond-mat↗

arXiv1997

Mean Field Dynamical Exponents in Finite-Dimensional Ising Spin Glass

We report the value of the dynamical critical exponent z for the six dimensional Ising spin glass, measured in three different ways: from the behavior of the energy and the susceptibility with the Monte Carlo time and by studying the overlap-overlap correlation function as a function of the space and time. All three results are in a very good agreement with the Mean Field prediction z=4. Finally we have studied numerically the remanent magnetization in 6 and 8 dimensions and we have compared it with the behavior observed in the SK model, that we have computed analytically.

cond-mat.dis-nn↗

arXiv1996

Dynamic fluctuations in a Short-Range Spin Glass model

We study the dynamic fluctuations of the soft-spin version of the Edwards-Anderson model in the critical region for $T\rightarrow T_{c}^{+}$. First we solve the infinite-range limit of the model using the random matrix method. We define the static and dynamic 2-point and 4-point correlation functions at the order $O(1/N)$ and we verify that the static limit obtained from the dynamic expressions is correct. In a second part we use the functional integral formalism to define an effective short-range Lagrangian $L$ for the fields $δQ^{αβ}_{i}(t_{1},t_{2})$ up to the cubic order in the series expansion around the dynamic Mean-Field value $\overline{{Q}^{αβ}}(t_{1},t_{2})$. We find the more general expression for the time depending non-local fluctuations, the propagators $[\langleδQ^{αβ}_{i}(t_{1},t_{2}) δQ^{αβ}_{j}(t_{3},t_{4})\rangle_ξ]_{J}$, in the quadratic approximation. Finally we compare the long-range limit of the correlations, derived in this formalism, with the correlations of the infinite-range model studied with the previous approach (random matrices).

cond-mat↗