Related papers: Exact mapping of a spin glass with correlated diso…
The effect of correlations in disorder variables is a largely unexplored topic in spin glass theory. We study this problem through a specific example of correlated disorder introduced in the Ising spin glass model. We prove that the…
Using the dedicated computer Janus, we follow the nonequilibrium dynamics of the Ising spin glass in three dimensions for eleven orders of magnitude. The use of integral estimators for the coherence and correlation lengths allows us to…
A periodic Ising model is one endowed with interactions that are invariant under translations of members of a full-rank sublattice $\mathfrak{L}$ of $\mathbb{Z}^2$. We give an exact, quantitative description of the critical temperature,…
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…
The average energy of the Ising spin glass is known to have no singularity along a special line in the phase diagram although there exists a critical point on the line. This result on the model with uncorrelated disorder is generalized to…
We show that, above the critical temperature, if the dimension D of a given Ising spin glass model is sufficiently high, its free energy can be effectively expressed through the free energy of a related Ising model. When, in a large sense,…
We consider a class of gauge glass models with Gaussian disorder on the Nishimori line, including the Ising spin glass, the $XY$ gauge glass, the $Z_q$ gauge glass, and the gauge-invariant Potts model. We prove that the first and second…
Monte Carlo data of the two-dimensional Ising spin glass with bimodal interactions are presented with the aim of understanding the low-temperature physics of the model. An analysis of the specific heat, spin-glass susceptibility,…
We report a high-precision finite-size scaling study of the critical behavior of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass). We have thermalized lattices up to L=40 using the Janus dedicated computer. Our…
We consider two bidimensional classical Ising models, coupled by a weak interaction bilinear in the energy densities of the two systems; the model contains, as limiting cases, the Ashkin-Teller and the Eight-vertex models for certain values…
The spin-1/2 Ising-Heisenberg tetrahedral chain is exactly solved using its local gauge symmetry, which enables one to establish a rigorous mapping with the corresponding chain of composite Ising spins tractable within the transfer-matrix…
This paper reports numerical studies of a compressible version of the Ising spin glass in two dimensions. Compressibility is introduced by adding a term that couples the spin-spin interactions and local lattice deformations to the standard…
In order to investigate the effects of connectivity and proximity in the specific heat, a special class of exactly solvable planar layered Ising models has been studied in the thermodynamic limit. The Ising models consist of repeated…
We consider the spatial correlation function of the two-dimensional Ising spin glass under out-equilibrium conditions. We pay special attention to the scaling limit reached upon approaching zero temperature. The field-theory of a…
The critical inverse temperature of the mean-field approximation establishes a lower bound of the true critical inverse temperature in a broad class of ferromagnetic spin models. This is referred to as the mean-field bound for the critical…
Spin glasses, generally defined as disordered systems with randomized competing interactions, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those…
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…
We have found a simple criterion which allows for the straightforward determination of the order-disorder critical temperatures. The method reproduces exactly results known for the two dimensional Ising, Potts and $Z(N<5)$ models. It also…
We present analytical results for the strongly anisotropic random field Ising model, consisting of weakly interacting spin chains. We combine the mean-field treatment of interchain interactions with an analytical calculation of the average…
We introduce and study a simplification of the symmetric single-impurity Kondo model. In the Ising-Kondo model, host electrons scatter off a single magnetic impurity at the origin whose spin orientation is dynamically conserved. This…