Related papers: Hyperscaling violation in Ising Spin Glasses
We determine accurate values of ordering temperatures and critical exponents for Ising Spin Glass transitions in dimension 4, using a combination of finite size scaling and non-equilibrium scaling techniques. We find that the exponents…
We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated…
Extensive simulations are made of the spin glass susceptibility and correlation length in five dimension Ising Spin Glasses (ISGs) with Gaussian and bimodal interaction distributions. Once the transition temperature is accurately…
Extensive simulations are made on the bimodal Ising Spin Glass (ISG) in dimension four. The transition temperature is established using a combination of standard finite size scaling and of thermodynamic derivative peak data. Measurements in…
The correlation length plays a pivotal role in finite-size scaling and hyperscaling at continuous phase transitions. Below the upper critical dimension, where the correlation length is proportional to the system length, both finite-size…
In order to overcome the limitations of small system sizes in spin-glass simulations, we investigate the one-dimensional Ising spin chain with power-law interactions. The model has the advantage over traditional higher-dimensional…
Ising spin glasses with bimodal and Gaussian near-neighbor interaction distributions are studied through numerical simulations. The non-self-averaging (normalized inter-sample variance) parameter $U_{22}(T,L)$ for the spin glass…
In the simple [hyper]cubic five dimension near neighbor interaction Ising ferromagnet, extensive simulation measurements are made of the link overlap and the spin overlap distributions. These "two replica" measurements are standard in the…
In random percolation one finds that the mean field regime above the upper critical dimension can simply be explained through the coexistence of infinite percolating clusters at the critical point. Because of the mapping between percolation…
After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…
The gauge glass in dimensions 3 and 4 is studied using a variety of numerical methods, in order to obtain accurate and reliable values for the critical parameters. Detailed comparisons are made of the sensitivity of the different techniques…
Finite-size scaling above the upper critical dimension is a long-standing puzzle in the field of Statistical Physics. Even for pure systems various scaling theories have been suggested, partially corroborated by numerical simulations. In…
The non-equilibrium ageing behaviour of the 3D and 4D critical Ising spin glass is studied for both binary and gaussian disorder. The same phenomenology of the time-dependent scaling as in non-disordered magnets is found but the…
We provide a resolution of one of the long-standing puzzles in the theory of disordered systems. By reformulating the functional renormalization group (FRG) for the critical behavior of the random field Ising model in a superfield…
Following numerous earlier studies, extensive simulations and analyses were made on the continuous interaction distribution Gaussian model and the discrete bimodal interaction distribution Ising Spin Glass (ISG) models in dimension two…
We show that current estimates of the critical exponents of the three-dimensional random-field Ising model are in agreement with the exponents of the pure Ising system in dimension 3 - theta where theta is the exponent that governs the…
We study the link overlap between two replicas of an Ising spin glass in three dimensions using the Migdal-Kadanoff approximation and scaling arguments based on the droplet picture. For moderate system sizes, the distribution of the link…
From a consideration of high temperature series expansions in ferromagnets and in spin glasses, we propose an extended scaling scaling scheme involving a set of scaling formulae which express to leading order the temperature (T) and the…
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…
Numerical investigation of critical exponents on a hypercubic with L^d random sites with L up to $33 and d up to 7 show that above the critical dimension the phase transitions in Ising model and percolation are not alike.