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Contrary to the suggestion of Kitatani and Sinada (2000 J. Phys. A: Math. Gen. {\bf 33} 3545-3553), the scaling analysis of the order parameter distributions suggests the existence of a finite-temperature spin-glass phase transition $T_c\ne…
A new method to numerically calculate the $n$th moment of the spin overlap of the two-dimensional $\pm J$ Ising model is developed using the identity derived by one of the authors (HK) several years ago. By using the method, the $n$th…
We study the order parameter distribution P(q) in the 4d Ising spin glass with $\pm J$ couplings in a magnetic field. We also compare these results with simulations for the infinite ranged model (i.e. SK model.) Then we analyse our…
A novel order parameter $\Phi$ for spin glasses is defined based on topological criteria and with a clear physical interpretation. $\Phi$ is first investigated for well known magnetic systems and then applied to the Edwards-Anderson $\pm J$…
We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character…
We present a numerical study of the order-parameter fluctuations for Ising spin glasses in three and four dimensions at very low temperatures and without an external field. Accurate measurements of two previously introduced parameters, A…
We propose a numerical criterion which can be used to obtain accurate and reliable values of the ordering temperatures and critical exponents of spin glasses. Using this method we find an value of the ordering temperature for the $\pm J$…
The critical properties of short-range Ising spin-glass models, defined on a diamond hierarchical lattice of graph fractal dimension $d_{f}=2.58$, 3, and 4, and scaling factor 2 are studied via a method based on the Migdal-Kadanoff…
Critical finite-size scaling functions for the order parameter distribution of the two and three dimensional Ising model are investigated. Within a recently introduced classification theory of phase transitions, the universal part of the…
We study the probability distribution P(M) of the order parameter (average magnetization) M, for the finite-size systems at the critical point. The systems under consideration are the 3-dimensional Ising model on a simple cubic lattice, and…
We demonstrate that the analytic calculation of the 1RSB break point parameter in a paper by de Oliveira and Fontanari[1] is erroneous, due to the omission of a higher order term in a lengthy perturbative calculation, and provide a…
The multicritical behavior at the Nishimori point of two-dimensional Ising spin glasses is investigated by using numerical transfer-matrix methods to calculate probability distributions $P(C)$ and associated moments of spin-spin correlation…
Within the Bethe- Peierls method the for short- ranged Ising spin glass, recently formulated by Serva and Paladin, the equation for the spin glass parameter function near the transition to the paramagnetic phase has been carried out. The…
This paper describes the application of finite-size scaling concepts to domain growth in systems with a non-conserved order parameter. A finite-size scaling ansatz for the time-dependent order parameter distribution function is proposed,…
We study the four dimensional (4D) $\pm J$ Ising spin glass in a magnetic field by using the simulated tempering method recently introduced by Marinari and Parisi. We compute numerically the first four moments of the order parameter…
The application of the collective variables method to the study of the behaviour of nonuniversal characteristics of the system in the critical region is illustrated by an example of the order parameter. Explicit expressions for the order…
We briefly review the use of the order parameter probability distribution function as a useful tool to obtain the critical properties of statistical mechanical models using computer Monte Carlo simulations. Some simple discrete spin…
Scaling arguments and precise simulations are used to study the square lattice $\pm J$ Ising spin glass, a prototypical model for glassy systems. Droplet theory predicts, and our numerical results show, entropically-stabilized long range…
This article is a contribution to the understanding of fluctuations in the out of equilibrium dynamics of glassy systems. By extending theoretical ideas based on the assumption that time-reparametrization invariance develops asymptotically…
The multifractal properties of the Edwards-Anderson order parameter of the short-range Ising spin glass model on d=3 diamond hierarchical lattices is studied via an exact recursion procedure. The profiles of the local order parameter are…