Related papers: Replica bound for Ising spin glass models in one d…
The fractal dimension of excitations in glassy systems gives information on the critical dimension at which the droplet picture of spin glasses changes to a description based on replica symmetry breaking where the interfaces are space…
Dilute dipolar Ising magnets remain a notoriously hard problem to tackle both analytically and numerically because of long-ranged interactions between spins as well as rare region effects. We study a new type of anisotropic dilute dipolar…
Using Monte Carlo simulations (MCS) and the Migdal-Kadanoff approximation (MKA), Marinari et al. study in their comment on our paper the link overlap between two replicas of a three-dimensional Ising spin glass in the presence of a coupling…
We analyze the infinite range Ising spin-glass in a transverse-field below the critical temperature by a one step replica symmetry theory(1S-RSB). The set of n replicas is divided in r blocks of m replicas each. We present results for…
We study the low-temperature spin-glass phases of the Sherrington-Kirkpatrick (SK) model and of the 3-dimensional short range Ising spin glass (3dISG). For the SK model, evidence for ultrametricity becomes clearer as the system size…
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…
Two, replica symmetry breaking specific, quantities of the Ising spin glass --- the breakpoint x1 of the order parameter function and the Almeida-Thouless line --- are calculated in six dimensions (the upper critical dimension of 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…
A dimer mean-field model for the Ising spin-glass is presented. Despite its simplicity it captures some of the essential features of the spin-glass physics. The distribution of the single-spin magnetization is determined from a…
We present a massive equilibrium simulation of the three-dimensional Ising spin glass at low temperatures. The Janus special-purpose computer has allowed us to equilibrate, using parallel tempering, L=32 lattices down to T=0.64 Tc. We…
We use the replica method in order to obtain an expression for the variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the presence of random external fields. Introducing a global order parameter, in the…
The concept of replica symmetry breaking found in the solution of the mean-field Sherrington-Kirkpatrick spin-glass model has been applied to a variety of problems in science ranging from biological to computational and even financial…
We study the behavior of droplets for two dimensional Ising spin glasses with Gaussian interactions. We use an exact matching algorithm which enables study of systems with linear dimension L up to 240, which is larger than is possible with…
Finite-size effects in the mean-field Ising spin glass and the mean-field three-state Potts glass are investigated by Monte Carlo simulations. In the thermodynamic limit, each model is known to exhibit a continuous phase transition into the…
We study the three-dimensional quantum Ising spin glass in a transverse magnetic field following the evolution of the bond probability distribution under Renormalisation Group transformations. The phase diagram (critical temperature $T_c$…
The replica method has been used to calculate the interface free energy associated with the change from periodic to anti-periodic boundary conditions in finite-dimensional p-spin glass models in the phase which at mean-field level has…
Results are presented for the geometry of low-energy excitations in the one-dimensional Ising spin chain with power-law interactions, in which the model parameters are chosen to yield a finite spin-glass transition temperature. Both…
In this paper, we extend the full replica symmetry breaking scheme to the Ising spin glass on a random regular graph. We propose a new martingale approach, that overcomes the limits of the Parisi-M\'ezard cavity method, providing a…
We present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random $p$-uniform hypergraphs with sparsity parameter $\alpha$. Our result shows that there exist two key regimes in which…
A longstanding open question in the theory of disordered systems is whether short-range models, such as the random field Ising model or the Edwards-Anderson model, can indeed have the famous properties that characterize mean-field spin…