Related papers: Inequality for local energy of Ising models with q…
We suggest a possible approach to proving the M\'ezard-Parisi formula for the free energy in the diluted spin glass models, such as diluted K-spin or random K-sat model at any positive temperature. In the main contribution of the paper, we…
We extend the self-consistent Ornstein-Zernike approximation (SCOZA), first formulated in the context of liquid-state theory, to the study of the random field Ising model. Within the replica formalism, we treat the quenched random field as…
Systems with quenched disorder possess complex energy landscapes that are challenging to explore under the conventional Monte Carlo method. In this work, we implement an efficient entropy sampling scheme for accurate computation of the…
We consider the Ising model on a general tree under various boundary conditions: all plus, free and spin-glass. In each case, we determine when the root is influenced by the boundary values in the limit as the boundary recedes to infinity.…
We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and…
We study the free energy of a mean-field spin glass whose coupling distribution has power law tails. Under the assumption that the couplings have infinite variance and finite mean, we show that the thermodynamic limit of the quenched free…
The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The…
We study a finite range spin glass model in arbitrary dimension, where the intensity of the coupling between spins decays to zero over some distance $\gamma^{-1}$. We prove that, under a positivity condition for the interaction potential,…
We investigate and contrast, via the Wang-Landau (WL) algorithm, the effects of quenched bond randomness on the self-averaging properties of two Ising spin models in 2d. The random bond version of the superantiferromagnetic (SAF) square…
We study a $(1+1)$-dimensional semi-discrete random variational problem that can be interpreted as the geometrically linearized version of the critical $2$-dimensional random field Ising model. The scaling of the correlation length of the…
Replica field theory is used to study the n-dependent free energy of the Ising spin glass in a first order perturbative treatment. Large sample-to-sample deviations of the free energy from its quenched average prove to be Gaussian,…
The standard phase-ordering process is obtained by quenching a system, like the Ising model, to below the critical point. This is usually done with periodic boundary conditions to insure ergodicity breaking in the low temperature phase.…
If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the…
On locally tree-like random graphs, we relate the random cluster model with external magnetic fields and $q\geq 2$ to Ising models with vertex-dependent external fields. The fact that one can formulate general random cluster models in terms…
The full replica symmetry breaking free energy of the Ising spin glass on random regular graphs is given by the solutions of two auxiliary variational problems inside a global (physical) variational problem on the order parameter. In this…
Results of extensive Monte-Carlo simulations that investigate the out-of-equilibrium dynamics of the one-dimensional Ising spin glass model with a Gaussian bond-distribution are presented. At low enough temperatures a typical (interrupted)…
We study a spin system on a large box with both Ising interaction and Sherrington-Kirpatrick couplings, in the presence of an external field. Our results are: (i) existence of the pressure in the limit of an infinite box. When both Ising…
Analysis of extremal behavior of stochastic processes is a key ingredient in a wide variety of applications, including probability, statistical physics, theoretical computer science, and learning theory. In this paper, we consider centered…
We study an effective spin model derived perturbatively from random transverse-field Ising model on the pyrochlore lattice. The model consists of spin-configurations on the pyrochlore lattice, restricted to the spin-ice subspace, with spins…
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 $T_c$…